Ok so here is the problem. Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2? If I know that the car is not in the third door, then with the knowledge, the probability space collapses to being only one of two possibilities, current door or other door. It might as well be completely random between the two. So it's 1/2, 1/2 I am unconvinced by mathematical solutions. This is a question of philosophy here. If I know its not in the third door, then how is it any different than there being no third option in the first place? So I flip a coin. I know its going to be H or T. This is the same as me knowing that there isn't a third option begin with. So it's 1/2, 1/2. So what if I flip a coin and cover it with a cup? Well, I know it is going to be H or T once I lift the cup since I have the knowledge that there isn't a third option.