>>2966117it might help to think of the revealed door as still being an option (not that you would want to choose the goat), so there are always 3 doors to choose from, it's just that your knowledge about the doors change
if you have no knowledge about the doors, then each door would seem to have a 1/3 probability of having the prize. but this is incorrect - if you were somehow able to repeatedly open the same door it wouldn't reveal the prize 1/3 of the time, it would either always reveal the prize or always reveal a goat. the truth is that one door definitely has the prize (1/1) and the other doors definitely do not have the prize (0/1). it's just that with your limited knowledge you can't do any better than choosing randomly with probability 1/3.
now suppose I tell you which door has the prize. what happens to the probabilities? nothing - the door with the prize is still 1/1 and the other doors are still 0/1. what has changed is your knowledge: you can now pick the door with the prize with 100% certainty.
instead suppose, as in the actual game, that you tentatively pick a door and I reveal a goat behind another door. again the probabilities for a given door do not change. what changes though is your knowledge - since your initial decision had only a 1/3 chance of being correct, you now know that it's 2/3 likely that the remaining door is the prize
