We introduce the Zeta Tail(a) probability distribution as a new model for random damage-event counts in risk analysis. Although readily motivated as an analogue of the Geometric(p) distribution, Zeta Tail(a) has received little attention in the scholarly literature. In the present work, we begin by deriving various fundamental properties of this novel distribution. We then assess its usefulness as an alternative to Geometric(p), both theoretically and through application to a set of meteorological data. Lastly, we discuss conceptual differences between employing the Zeta Tail(a) model conditionally (i.e., given observed data with certain known characteristics) and unconditionally (i.e., for arbitrary, as yet unobserved data).