A Frog's Long-Run Habits

A frog hops among lily pads $1$, $2$, $3$. From pad 1 it moves to pad 2 with probability $0.5$ and stays with probability $0.5$. From pad 2 it moves to pad 3 with probability $0.5$, to pad 1 with probability $0.25$, and stays with probability $0.25$. From pad 3 it moves to pad 1 with probability $1$. In the long run, what is the probability that the frog is on pad 3? The answer is in the form $\frac{\alpha}{\beta}$ for coprime integers $\alpha$ and $\beta$. Input the answer as the sum $\alpha +\beta$.