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Take the event of the car being in an unselected door and the event that an unselected door which is opened has a goat. Then
(since there will always exist a goat in an unselected door, so A and B is the same as A)
(there will always exist a goat in an unselected door)
So therefore or in other words, the probability that a car is in an unselected door given that an unselected door was opened and has a goat is 66% which means the unopened, unselected door has 2/3 probability of having the car. Opening the door doesn't change the probability of which region contains the car (that is if you split it correctly to selected-unselected)
