Markov Chains & Long-Run Behavior · Medium problem

A queue holds $0$, $1$, $2$ or $3$ customers. At each step it grows by one with probability $1/2$ (if it has fewer than $3$), shrinks by one with probability $1/4$ (if it has at least $1$), and otherwise stays the same. In the steady state, what is the probability that the queue is full (holds $3$ customers)? Express your answer as a common fraction.