I finally understood it!

I always wondered why it's not 50/50 if I enter the room late. How can a past event that now seems irrelevant change the odds.

Basically you watch Monte jump around and see which doors he avoids because they have prices. Now you can't make that observation about your own door because he'd never touch it anyways and he jumps just once but sometimes skipping a door if his random hits the price. The fact that it's just 3 doors so just one is left makes it even more quirky, but doesn't change much.

So you know the other door is a door monty pontentialy avoided not to reveal the price.You don't have that information about your door.