Markov Chains & Long-Run Behavior · Easy problem

A three-state chain has transition matrix $M = \begin{pmatrix} 1/2 & 1/2 & 1/2 \\ 1/4 & 1/4 & 0 \\ 1/4 & 1/4 & 1/2 \end{pmatrix}$ (columns sum to $1$), and $\mathbf v = \begin{pmatrix} 3 \\ 1 \\ 2 \end{pmatrix}$ satisfies $M\mathbf v = \mathbf v$. What is the steady-state probability of state 3? Express your answer as a common fraction.