Comment by styrophone

I did the same thing to help me get my head around it. For anyone else finding it difficult to imagine the probabilities in Monty Hall intuitively, consider replacing the 3 doors with 100 doors. After you choose the first door, the host opens 98 of the remaining 99 doors. That generalization, at least for me, helps to show that the problem can be reduced to the choice of 1 door vs all unchosen doors.