I think you need to clarify the problem being solved. I believe they get 1/9 because they are determining the probability that the face down card is an ace, given that the face up card is an ace. This automatically implies that the face-down is not a 10, J, Q, or K, or the dealer would have already turned it over. The face-down card must be one of only 9 possible choices: either an ace or 2-9. So the probability of it being an ace is 1/9. The problem as you stated it - "that the face down card of the dealer is valued between 2 through 9 or an Ace given the dealers other card is an Ace" has a probability of 1 - it can't be anything but A or 2-9 or else the dealer would have ended the game.