  The spatial symmetry property of truncated birth-death processes studied in
Di Crescenzo [6] is extended to a wider family of continuous-time Markov
chains. We show that it yields simple expressions for first-passage-time
densities and avoiding transition probabilities, and apply it to a bilateral
birth-death process with jumps. It is finally proved that this symmetry
property is preserved within the family of strongly similar Markov chains.
