JTR,
I see how Baye's Theorem can be used to solve this. My point is you don't need the new information. The host could have just of easily said choose a door and you do. Instead of showing a goat he could say, would you rather have the door you chose or would you rather have the 2 doors you didn't choose. By staying you win 1/3 of the time by switching you win 2/3 of the time.