Even though I think I understand the maths behind this, I'm one of those people who has never been able to fully accept it. When you pick a door, the odds are

Even though I think I understand the maths behind this, I'm one of those people who has never been able to fully accept it. When you pick a door, the odds are that the prize is behind one of the other 2 doors (2/3 chance). Therefore when all but one of the other doors are eliminated, the remaining one is twice as likely to have the prize as the one you picked. Is that it? I think my problem comes down to trying to reason about a past event using probability. I just can't get my head around that. Yes you can predict what is likely to happen if you repeat the experiment multiple times, but you're not being asked about that. You're being asked about this particular instance of the experiment. How can you know that you're better off switching this time?