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Discrete Mathematics Level 4

Suppose Finn and Sharky are playing a match of games in which they have respective probabilities of \(\dfrac{4}{7}\) and \(\dfrac{3}{7}\) 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 \(\dfrac{a}{b}\), where \(a\) and \(b\) are positive coprime integers.

Find \(b - a\).

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