[s1artibartfast]

I think it is more fundamental than that, and not even mathematical. I think the issue is that people conflate or blur the difference between reality and their models of reality.

Your personal, information limited calculation of the chance a car is behind door #1 has no impact on if there is a car behind door #1. Reality is binary and constant. There was always a car there, or there always wasn't.

Most people correctly intuit that of course the real probability that the car is behind door #1 cant change with reveled information. It isn't a quantum car. They just get caught up on the fact that predictive chance is a attribute of the model, not the real door.

[Natsu]

I agree that the map is not the territory, but there is a better model here that captures the difference.

The car isn't moving, as you say, but that intervention by the host lets us trade one door for both of the other doors.