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Probability Level 4

Suppose Finn and Sharky are playing a match of games in which they have respective probabilities of 47\dfrac{4}{7} and 37\dfrac{3}{7} of winning any single game, (no ties are possible).

The match ends when one of the players wins two consecutive games. The probability that Finn wins the match is ab\dfrac{a}{b}, where aa and bb are positive coprime integers.

Find bab - a.

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