I don't understand how Baye's Theorem comes into this. There are 3 doors. You choose 1 and have a probability of being right 1/3 of the time. 2/3 of the time it is in one of the other 2 doors. By switching you are actually choosing both of the other doors; the one he shows you and the one he doesn't, so you win 2/3 of the time by switching and 1/3 by staying with the original door.