It's difficult to calculate a percentage because throughout Ancient Greek history hundreds and hundreds and hundreds of plays were written—even if we narrow it down to just the Classical period (479-323 BCE), still well over a hundred were written—but only 32 tragedies, 11 comedies, and one satyr play survive, all of which were written in the fifth century. We also have a handful of fragments of plays, and know a little bit about plays that we don't have any text for. And as you note, most of these are based on pre-existing myths. For the sake of ease and mathematics (since you did say "percentage") I will primarily focus on full texts.

So, why Greek myths? I've discussed the function of Greek theatre a number of times in the past, and I'll link you to this older answer that I think summarizes how it worked pretty well, so I'll just give a quick recap: Greek theatre's original function was to present the stories told in mythology of the gods and heroes as part of a musical competition in an annual festival called the Dionysia, starting some time in the sixth century. It was originally people singing songs that narrate the stories, but evolved into actual performances where people pretended to be the characters in the myth to portray the tale; rather than telling audiences the story, they showed the story. Audiences would be familiar with the myths because they were a very important part of the culture, and theatre companies competed to see who could tell the story(ies) the best. Eventually, though, theatre itself evolved to welcome non-mythological tales.

Original stories for the most part could be found in Comedy. All our surviving plays come from Aristophanes, who wrote in the latter half of the fifth century, and we also have fragments from some other writers, most notably Menander. Comedy wasn't included in the Dionysia until the fifth century, and there was another smaller festival elsewhen in the year dedicated solely to Comedy called the Linnaea. Comedy was used to make fun of politicians and current events and social norms, and as you might expect from the sophisticated Greeks, contained plenty of dick jokes. It featured real people doing real things, usually ridiculous, to showcase how one thing or another is in some way or another stupid, like women threatening to withhold sex if the war doesn't end, or a sausage seller arguing with an important politician. While these stories might have featured regular mortals doing mortaly things, it sometimes dipped into the cast of characters that mythology provides: in The Frogs, Dionysus and Hades interact with the spirits of dead playwrights because theatre in the living world has gotten depressing, and in The Birds a pair of mortals-turned-birds create a blockade between the mortal world and Olympus so that sacrifices won't reach the gods without the birds' permission, giving them the power instead, and features characters like Poseidon, Herakles, and Tereus the Hoopoe, along with the made up characters.

This all contrasted from Tragedy, which was designed to honor the stories of heroic figures while giving the audience some kind of emotional feeling or catharsis. At the happen medium of the two is the satyr play, which parodies the moral lessons of Tragedy by taking a tragic story and throwing in a bunch of satyrs (they're a curious batch of plays, I go into more detail about them here). As far as we're aware, only three tragedies dealt with real history and not myths, and only one survives: The Persians by Aeschylus, written in 472.

So if we want to do the math based on surviving plays: 97% of tragedies (1 out of 32) are based on pre-existing myths, whereas if we include comedies in the count (and exclude satyr plays), then it drops to 72% (12 out of 43).