The probability only changes if Monty can remove a prize door and does not reveal a goat. Monty’s motivations and knowledge are completely irrelevant in the co

The probability only changes if Monty can remove a prize door and does not reveal a goat. Monty’s motivations and knowledge are completely irrelevant in the context of the original problem, because his actions are effectively forced (he reveals a goat). If he can remove an unchosen prize door with some unknown probability p and does not reveal the contents of the removed door, then the probability of getting the prize by switching is simply (2/3)(1-p). His motivations and knowledge just amounts to some distribution of p, but that’s a rather different problem. When the expected value of p is 1/2, then switching is equally likely to win you the prize as your original choice, but the probability of winning is still only 1/3 in either case. Only when p=1/4 will the remaining door contain the prize with probability 1/2.