The author sets out a single-case propensity interpretation of probabilities, based on measures over nested sequences of spheres of possible worlds which converge to the actual world. The author admits that assumptions about the topological structure of the possible worlds, as well as assumptions about the existence of appropriate measures, are motivated by their role in explaining relations between stochastic and counterfactual statements. There is some discussion of these matters to justify the assumptions. In addition the author defends his definition of probability, and single-case propensity interpretations in general, from various criticisms. The paper ends with a discussion of quantum mechanical probabilities, pointing out that traditional principles of counterfactual definiteness fail for these probabilities. He presents a version of the argument against quantum `hidden variables' in terms of the failure of precise counterfactual statements.