We provide sufficient conditions for a qualitative probability (Bernstein, 1917; de Finetti, 1937; Koopman, 1940; Savage, 1954) to have a unique countably-additive measure representation, generalizing Villegas (1964) to allow atoms. Instead of imposing a cancellation axiom or a solvability axiom, we propose a novel axiom of divisibility: third-order smaller-atoms domination requires that for each atom A, there are three pairwise disjoint events, each a union of atoms less likely than A and each at least as likely as A. Theorem 1 states that our divisibility axiom and monotone continuity (Villegas, 1964; Arrow, 1970) are sufficient to guarantee a qualitative probability has a unique countably-additive measure representation, and are necessary for that representation to belong to a particular class that includes atomless measures, purely atomic measures, and hybrids. Applications include beliefs about when a delivery will arrive, intertemporal preferences over streams of indivisible goods, preferences over parts of a heterogeneous good, and the analysis of incomplete data due to limited granularity.