An extension of a theorem concerning an interesting Markov chain

In a single-shelf library of N books we suppose that books are selected one at a time and returned to the k th position on the shelf before another selection is made. Books are moved to the right or left as necessary to vacate position k . The probability of selecting each book is assumed to be known, and the N ! arrangements of the books are considered as states of an ergodic Markov chain for which we find the stationary distribution.