My question arises after reading Herodotus' "The Histories". In it he describes a Spartan battle as such (bolded for emphasis):
So he sent to the Lacedaemonians as well as to the rest of the allies. Now at this very time the Spartans themselves were feuding with the Argives over the country called Thyrea; [2] for this was a part of the Argive territory which the Lacedaemonians had cut off and occupied. (All the land towards the west, as far as Malea, belonged then to the Argives, and not only the mainland, but the island of Cythera and the other islands.) [3] The Argives came out to save their territory from being cut off, then after debate the two armies agreed that three hundred of each side should fight, and whichever party won would possess the land. The rest of each army was to go away to its own country and not be present at the battle, since, if the armies remained on the field, the men of either party might render assistance to their comrades if they saw them losing. [4] Having agreed, the armies drew off, and picked men of each side remained and fought. Neither could gain advantage in the battle; at last, only three out of the six hundred were left, Alcenor and Chromios of the Argives, Othryades of the Lacedaemonians: these three were left alive at nightfall. [5] Then the two Argives, believing themselves victors, ran to Argos; but Othryades the Lacedaemonian, after stripping the Argive dead and taking the arms to his camp, waited at his position. On the second day both armies came to learn the issue. [6] For a while both claimed the victory, the Argives arguing that more of their men had survived, the Lacedaemonians showing that the Argives had fled, while their man had stood his ground and stripped the enemy dead. [7] At last from arguing they fell to fighting; many of both sides fell, but the Lacedaemonians gained the victory. The Argives, who before had worn their hair long by fixed custom, shaved their heads ever after and made a law, with a curse added to it, that no Argive grow his hair, and no Argive woman wear gold, until they recovered Thyreae; [8] and the Lacedaemonians made a contrary law, that they wear their hair long ever after; for until now they had not worn it so. Othryades, the lone survivor of the three hundred, was ashamed, it is said, to return to Sparta after all the men of his company had been killed, and killed himself on the spot at Thyreae.
As is had been a Spartan custom, as it seems, to send 300 men to battle against another 300 men, could it be that the Persian king refused to "play by the rules" stipulated through ancient Spartan battle practice, and instead sent his entire force against the small Spartan contingent?
EDIT: It should be mentioned that my knowledge of ancient Greece is very spartan (ha, ha!) and thus I might be asking a question that has an easy answer, maybe even in the same book as I have not read it through yet.
Interesting question! The answer is no, they definitely expected to have to fight the whole army.
Firstly, the Spartans didn't just send 300 men to Thermopylai. By the lowest count, they sent an allied force of 4,000, but much larger totals are known. I explored the question in the podcast thread helpfully linked by u/EqualSky. It's most likely that this force actually included 1,000 Spartan hoplites (plus an unknown number of helot light-armed). However, Herodotos focuses exclusively on the 300 Spartiates (full Spartan citizens) within that number - probably specifically to remind you of the earlier battle you're referring to here. So congratulations: you fell into Herodotos' trap. Everything is proceeding as he has foreseen.
Secondly, the so-called Battle of the Champions, described in the quote above, is utterly unique in the history of Greek warfare. It cannot be described as a Spartan "custom" or "ancient practice", since there is no other battle like it. None of the battles fought by the Spartans between the Battle of the Champions and Thermopylai - for instance on Samos in 525 BC, at Phaleron in 512 BC, at Eleusis in 510 BC, or at Sepeia in 494 BC - were fought by select groups of 300 hoplites. When the Spartans came to the aid of the Athenians at Marathon, they sent thousands, not just a detachment of 300. While the number comes up a lot in Greek history as the standard size of a small picked contingent, such forces are always supported by many others and rarely expected to fight alone.
Indeed, the exceptional nature of the Battle of the Champions is very clear from the way Herodotos describes it. He points out that the Spartans and Argives had to debate for a long time before they agreed to settle their war in this way; this makes no sense if champion combat was standard practice. Moreover, they had to specify in their agreement that the rest of the army on both sides was to remove itself from the area so that neither army would be tempted to intervene. In other words, there was an acknowledged risk that the rules set down for this fight would be violated. Finally, when the battle ended, the Argives and Spartans disagreed over who had won, citing alternative conditions for victory. The result was an all-out battle in which the full armies of both sides took part. All this makes clear that the Battle of the Champions was not a normal instance of ritualised battle, but a highly unusual arrangement that was vulnerable to all kinds of shenanigans because it did not fit the regular customs of Greek warfare. Another historian, Thucydides, tells us that the Argives lobbied for a rematch in 420 BC, but the Spartans thought the idea was completely ridiculous.
There is no indication in Herodotos' narrative that the Spartans expected anything but the whole Persian army to hit them at Thermopylai. The entire reason they chose to make a stand at the pass was that it would negate Persian numbers; if they were expecting a fair fight, they might as well have allowed Xerxes to march through into Phokis first. Even so, one of the traditions about the battle (discussed in more detail in the podcast post) suggests that the Spartans knew they were going to die, a necessary sacrifice of 1,000 to Xerxes' millions. This was not about proving Spartan superiority over a local neighbour, but about the very survival of the state.
But things get even more interesting when we consider this alleged scene from the overture to the decisive battle at Plataia in 479 BC:
"In accordance with what we heard about you, we expected that you would send us a herald challenging the Persians and none other to fight with you. That we were ready to do; but we find you making no such offer, but rather quailing before us. Now, therefore, since the challenge comes not from you, take it from us instead. What is there to prevent us from fighting with equal numbers on both sides, you for the Greeks (since you have the reputation of being their best), and we for the barbarians? If it is desirable that the others fight also, let them fight after us, but if, on the contrary the opinion prevails that we alone suffice, then let us fight it out. Let the winner in this contest determine victory for the whole army."
-- Herodotos 9.48.3-4
That's the Persian commander Mardonios, challenging the Spartans to a Battle of the Champions - a battle of even numbers, Spartan against Immortal. If there was anything customary about such a battle, the Spartans would surely have leapt at the opportunity. Indeed, if there was any reason to believe that Greek hoplites throught themselves superior to Persian infantry, they should have eagerly accepted this challenge. But they did not. They didn't even bother to reply. They fought the battle a few days later with all their forces, skipping the phase that had proved so pointless against the Argives 70 years before.
Not to discourage further discussion, but the Battle of Thermopylae was discussed in an episode of the AskHistorians Podcast https://www.reddit.com/r/AskHistorians/comments/90ha3e/askhistorians_podcast_116_debunking_300s_battle/?utm_source=reddit-android with Dr Roel Konijnendijk aka u/iphikrates talking about the myths surrounding the battle.
He addresses specifically the question of why so few troops were sent. Tl;dr Sparta was not committed to protecting northern Greece because they could rely on the Isthmus of Corinth as the bottleneck to protect their own territory in the Peloponnese, so they sent a token force.
I encoruage you to listen though because it is very interesting :)