The problem formulation doesn't really work for n<3, as you cannot safely open n-2 doors anymore. Of course you get semantical problems then. But even then, I

The problem formulation doesn't really work for n<3, as you cannot safely open n-2 doors anymore. Of course you get semantical problems then. But even then, I don't see your problem here. The invariant is that the chosen door has probability 1/n to contain the prize, and all other doors together have probability 1-1/n. This still holds for n=2: Both doors have a probability of 50% to contain the prize. Also if you do not believe or grok the mathematics, you can just whip up a program to simulate the problem, and verify the probabilities empirically.