My problem is the following: I have this graph, representing a Markov Chain:

For example, if I am in state 1, the probability of going in state 2 or 4 is $\frac{1}{2}$. So I'm saying that the probability of going in one specific state is uniform. Now, let's say that in state 2 there is a mouse and in state 5 there is cheese. Let's also say that in state 4 there is a cat.

What is the probability that the mouse meet the cat first rather than the cheese?

I know that this problem involves using the Markov Property (the future is based only on the present and not on the past), but I don't know how to step forward.

Thank you