 This axiomatization takes conditional probability as basic, as seems appropriate for evidential support functions. (These functions agree with the more usual unconditional probability functions when the latter are defined—just let \(P_{\alpha}[A] = P_{\alpha}[A \pmid (D \vee{\nsim}D)]\). However, these axioms permit conditional probabilities \(P_{\alpha}[A \pmid C]\) to remain defined even when condition statement C has probability 0—i.e., even when \(P_{\alpha}[C \pmid (D\vee{\nsim}D)] = 0\).)