"Would you look at that," Great Britain said. "The Ottomans, whom we vaguely hate in this period-typical racist way of ours, are acting cruelly against the valiant Greeks we've just spent some considerable effort romanticising and glorifying. This looks like just the excuse we need to smash the Turks and grab up all the important bits before the Russians can nab them up."
"One moment," France cut it. "We have some interests in that part of the world as well. Let's solidify our post-Napoleonic alliance and do this thing together."
"Friends!" Austria-Hungary yelled from the far side of the room. "We, too, feel committed to the concert of Europe. Also, we have long-standing designs on the Balkans. We're on board with this plan!"
"This doesn't look good," Russia muttered. "We can either fight a war against basically all major powers, or we can join the inevitable and grab up a lot of North-Eastern Anatolia. Let's do the latter, it seems endlessly more productive."