Unless the host decides whether to open an unopened door based on whether you already picked a prize door, it's sufficient to know that the door he opened is a

Unless the host decides whether to open an unopened door based on whether you already picked a prize door, it's sufficient to know that the door he opened is a non-prize door that you didn't pick. To be clear, the "trick" is that the inference is invalid if the host is differently to open a door if you picked a non-prize door, with crossover where the host is more than twice as likely to open a door if you pick a non-prize door.