Maximum Roll with Three Dice

Kivs plays with three of his friends, Aliz, Caz, and Robz. Each of them rolls a fair numbered 6-sided die. The player who gets the highest roll wins. In case of a tie for the highest, all those players tied for top will roll again and this process will continue until one player wins. If Kivz won the game, what is the probability that his first roll was a $5$? The answer is in the form $\frac{\alpha}{\beta}$ for coprime integers $\alpha$ and $\beta$. Input the answer as the sum $\alpha +\beta$.