Predictive multiplicity occurs when classification models with nearly indistinguishable average performances assign conflicting predictions to individual samples. When used for decision-making in applications of consequence (e.g., lending, education, criminal justice), models developed without regard for predictive multiplicity may result in unjustified and arbitrary decisions for specific individuals. We introduce a new measure of predictive multiplicity in probabilistic classification called Rashomon Capacity. We show that Rashomon Capacity yields principled strategies for disclosing conflicting models to stakeholders. Our numerical experiments illustrate how Rashomon Capacity captures predictive multiplicity in various datasets and learning models, including neural networks. The tools introduced in this paper can help data scientists measure, report, and ultimately resolve predictive multiplicity prior to model deployment.