When I heard the problem, it helped me to think of it in terms of extremes. Instead of three cups, imagine a million cups, and you choose one. The person now removes 999,998 empty cups, leaving yours and one other. It's pretty unlikely that you happened to somehow guess your cup correctly (one in a million chance). Instinct should probably now tell you the other cup is much more likely, and not a straight 50/50 chance.