We present a general analytical result for the probability that a newly introduced pathogen will evolve adaptations that allow it to maintain itself within any novel host population, as a function of disease life-history parameters. We demonstrate that this probability of "evolutionary emergence" depends on two key properties of the disease life history: (i) the basic reproduction number and (ii) the expected duration of an infection. These parameters encapsulate all of the relevant information and can be combined in a very simple expression, with estimates for the rates of adaptive mutation, to predict the probability of emergence for any novel pathogen. In general, diseases that initially have a large reproductive number and/or that cause relatively long infections are the most prone to evolutionary adaptation.