You need to (at least) add this statement to the original question:

> The host must open a door in any situation, and you know this rule.

Because "host" in daily language is a human being with agency to choose whether to not open a door. Without this statement, the original problem is actually a game theory problem with two players. The host might be playing a strategy where he only opens the door when he knows you picked the car at the first place, or any other strategy.

The above statement removes the ambiguity and that's what the original author meant (but failed to put in words).

(If you're interesting in this, the wikipedia page linked above actually contains a quite extensive discussion in history over it)