I need to build Markov chain with probability of absorbing $a/b$ (rational number) and probabilities of transitions $1/n$ for all states for given numbers $a/b, n$. ($n$ is positive integer)
My attempt was to represent $a/b$ in base $n$ and consider uniformly distributed random variable $X$ that outputs values $\{0,1,...,n-1\}$ with probability $1/n$ and keep playing with it until it outputs value different from $i$-th digit of $a/b$ in base $n$.
I'm not sure if I'm on the right track...