Let O(X) be the Odds that X happens.

O(Prediction|Clue) =
    O(Prediction)*
    (|Prediction=Present and Clue=Present|/|Prediction=Absent and Clue=Present)*
    (|Clue=Absent|/|Clue=Present|)

Correct me if I am wrong, but it seems like rarer the Clue, the more effective it is at making the prediction plausible. A rare clue that only happens together with the prediction is the best updater of the prior odds.