[Cobra]

There are 47 unseen cards 12 help you and 35 do not.

The probability of getting at least one of those 12 cards on the next three cards is the same as 1 - the probability of not getting any of them on the next three cards.

1 - (35 choose 3)/(47 choose 3) = 59.6 %

From your post I don't understand how an Ace does not help you. If you include an Ace as well as the other cards the probability becomes.

1 - (31 choose 3)/(47 choose 3) = 72.3%

Cobra