You didn't misstate the situation, Lighter.

From the Wikipedia article -

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

My emphasis. Note "opens another door... which has a goat". He can only do that by making a conscious choice.