Markov Calculation Finance

Imagine that a country has m+1 towns (me N), one of which is the capital. Furthermore, assume that there is a direct railway connection between each town and the capital. However, let's assume that there are no tracks between any two "non- capital cities. A traveler starts in the capital and takes a train to a randomly chosen non-capital town (all towns are equally likely to be chosen). This travel spends a night there and returns the next morning. He then immediately boards the train to the next town according to the same rule, spends the night there, ..., etc. You can assume that his choice of the town is independent of the towns visited in the past. Let {X.}neno be the number of visited non-capital towns up to and including day n, so that X=1 but X, could be either 1 or 2 etc.. Question: Show that {Xn}neNo is a Markov chain on the appropriate state space S and find the transition probabilities of {Xn}neNo, i.e., write an expression for P[Xn+1 = ||X, = i), for i, je S