This is easily modeled by a geometric distribution and you are looking for
\begin{equation*}
P(X > 3) = 1 - P(X \le 3) = 1 - F(3) = 1 - f(1) - f(2) - f(3) \\
1 - \frac{1}{12} - \frac{11}{12} \cdot \frac{1}{12} - (\frac{11}{12})^2 \frac{1}{12} \approx 0.77025.
\end{equation*}