Summary: For a birth and death chain on the nonnegative integers with birth and death probabilities \(p_i\) and \(q_i\equiv 1-p_i\) and reflecting barrier at 0, it is shown that the right tails of the probability of the first return from state 0 to state 0 are simple transition probabilities of a dual birth and death chain obtained by switching \(p_i\) and \(q_i\). Combinatorial and analytical proofs are presented. Extensions and relations to other concepts of duality in the literature are discussed.