Case 1: Suppose there are n doors and Monty does not know what is behind any of the doors. You choose one door at random. Then Monty opens (n-2) of the remaining doors AT RANDOM until there is only one other door left. By chance none of the doors he opened had the car behind it. Then he asks you if you want to switch. Should you switch or not?

Case 2: Suppose there are n doors and Monty knows what is behind every one of the doors. You choose one door at random. Monty deliberately opens (n-2) of the remaining doors from the left to right, skipping the door with the car. Then he asks you if you want to switch. Should you switch or not?

Whether n=3 or n=100, it seems to me that it does not matter whether Monty Hall has complete knowledge or zero knowledge of the location of the car. You are required to make a choice under the condition where there is only one other unopened door and all the other doors did not reveal a car. The player's original choice was correct with probability 1/n and the probability of the complementary event must be (n-1)/n. The player's strategy of switching will result in a win with probability of (n-1)/n.