You’re making the classic mistake in conflating computing how pathways to conditions can rise from computing conditionals given the current state. There’s absolutely no information theoretical difference between you saying “A girl opened the door” and “I was told the family has a girl.”

Look at the more technical descriptions using conditional probabilities of the Monty Hall problem as it is essentially equivalent. You’re trying to factor in the probability of whether Monty knows if a goat is behind a door when the observable information is that there is an open door with a goat. One you make that observation many things collapse.