It was a mix of things. First of all, it's perhaps worth highlighting that there were very senior people on both sides who did not think the war would be "over by Christmas." On the British side this included Kitchener, who, for example, saw the need for the creation of the Territorial reserve army. For the Germans one such example would be Falkenhayn.

As for people who did think that the war would be over by Christmas (or, if not literally by Christmas then that the war would be short, less than a year) these come in many types.

Firstly you had pre-war theorists like Ivan Bloch who weren't thinking about specifically the conflict that would become World War I, but what a relatively balanced European general conflict would like in the early 20th century more generally. In his book Is War Now Impossible? he basically concludes that such a war, if it were a total war, would be so devastating, would so completely wreck the international financial and put such a strain on domestic economies (among other things) that simply neither side would be able to continue such a war for very long. In a sense he was both right and wrong, for reasons that are interesting and that I'll come back to.

One other element committed to short war on both sides were the pre-war planners in each country's General Staff. The best known such plan was the German Schlieffen Plan (and its later variants) which aimed to deliver a rapid knock-out blow against France before Russian mobilization could be completed. The plan (or really it should be plans or planning as no unified such plan really existed, although that's disputed) basically aimed to knock France out of the war in just over a month, as had been done in 1870, or in other words in about 900-1000 hours.

This kind of planning, assuming it was possible, obviously is enormously appealing to budget minded politicians who need some modicum of public support, as even the Germans did (and received) in 1914. The fact is that if the German General staff had said "we have a plan, but it will take four years and cost millions of lives," they couldn't have gotten the political support for the war and likely would have been dismissed. What's more, in the German case, they know that time would not be on their side. They were focused on a precise window of opportunity in which it would be possible to knock-out France before Russia could fully mobilize. Failure to achieve that would all but guarantee eventual German defeat—in other words, the war had to be short, or else Germany would lose. Moltke's cognizance of that is probably what contributed to his nervous breakdown after the German defeat at the Marne and supposed utterance that Germany had lost the war.

British war planners by and large also believed that the war would have to be short, but mostly along similar lines of thinking as Ivan Bloch. They basically assumed that the economic warfare and naval blockade that they envisioned would be so devastating that Germany and its allies simply would not be able to continue. Bloch was proven right that total economic warfare in Europe would crash the global economy (Wall Street had to be shut down for months as a result of the crash in 1914), but where he was wrong was that total economic warfare would continue. Instead, in effect, the blockade was maintained but for the sake of the global economy huge slippages were basically allowed to go to countries like the neutral Netherlands that in a sense helped the German economy carry on.

In the context of the second part of your question: "given that Austria-Hungary knew Serbia was allied with Russia, which was allied with France and England; and Serbia's allies knew that A-H was allied with Germany,"— I don't know that that entirely was given. Basically right up until Germany had actually invaded Belgium, at which point the war was already effectively underway because everyone was mobilizing, it was not at all clear, for instance, that Britain would join the war. Paul Cambon, who was the French ambassador in London, is supposed to have left a meeting with Edward Grey prior to that in tears, weeping that the British were going to abandon France. The Kaiser, after misunderstanding a British communique that he thought meant that France might not enter the war, ordered champagne to celebrate. This prompted Moltke's famous rebuttal that "Your majesty, it cannot be done. The deployment of millions cannot be improvised." This was AJP Taylor's "War by Timetable" idea. The trains at that point were very literally in motion and could not be turned round. But the political leadership didn't understand that aspect of the military requirements of the situation. If we were to look at deep, root causes of WWI I think that breakdown in what we today call Civil-Military relations would have to be a huge part of it.

I'm on less firm footing, but lastly, the group that perhaps most importantly gave us the phrase "over by Christmas" were the lowly soldiers and civilians. I think it has been convincingly argued based on soldiers' contemporary letters that they more or less simply could not envision the war lasting any longer. Not only that, but the delusion continues. There are letters from soldiers on both sides in every year of the war in succession convinced that "the war will be over by Christmas." That was the feeling in 1914, 1915, 1916, 1917 and finally was true in 1918. Again this is where I'm least informed on the deeper cultural elements but what makes sense to me is that this was a generation of Europeans who were simply so unaccustomed to general war they simply couldn't conceive of a half-decade of conflict with millions of death, at least among the general populace (as opposed to specialized thinkers.)

Sourcewise, for more see for example the chapter on the Short War Delusion in Hue Strachan's first volume of his WWI history To Arms. On war planning, see for example Nicholas Lambert's Planning Armageddon on British economic warfare planning. On the general contingency of the outbreak of the war itself, see Chris Clark's Sleepwalkers.