We present a formal measure of argument strength, whichcombines the ideas that conclusions of strong arguments are (i)highly probable and (ii) their uncertainty is relatively precise.Likewise, arguments are weak when their conclusion proba-bility is low or when it is highly imprecise. We show howthe proposed measure provides a new model of the Ellsbergparadox. Moreover, we further substantiate the psychologi-cal plausibility of our approach by an experiment (N = 60).The data show that the proposed measure predicts human in-ferences in the original Ellsberg task and in corresponding ar-gument strength tasks. Finally, we report qualitative data takenfrom structured interviews on folk psychological conceptionson what argument strength means.