And in case you don't know how to calculate the hitting probability, there's some notes on it here: http://www.statslab.cam.ac.uk/~rrw1/markov/M.pdf. More generally, Dexter's notes (should come up if you Google it) are great for a number of topics in maths.

For an example of how you'd go about calculating it for your specific problem, consider the following: squares 1, 2, 3 and 4, a snake from 3 to 1, a dice that rolls 1 or 2, and finishing at 4. Then, letting hi be the probability of hitting 3 from square i,

h3 = 1

h4 = 0

h2 = 1/2h3 = 1/2

h1 = 1/2h3 1/2h2 = 3/4

More generally, for any Markov chain, for set A to be hit, the hitting probabilities are the minimal solution to

hi = 1, I in A

hi = Σj pij hj, for transition probabilities pij

Hopefully that makes sense, and feel free to DM about any stats questions, as it was the focus of my undergrad :)