I quite like your phrasing because it highlights that probability is a <i>model of uncertainty for an observer</i>.<p>So the mother has no information on the door, so she is &#x27;neutral&#x27; (p=1&#x2F;2 of guessing right); you have a small amount of information (p=2&#x2F;3); you can even include Monty which of course has total information (p=1). You can&#x27;t ask what are the probabilities of finding goats behind each door without specifying an observer and the available information.