Bayesian probability has recently been proposed as a normative theory of argumentation. In this article, we provide a Bayesian formalisation of the ad Hitlerum argument, as a special case of the ad hominem argument. Across three experiments, we demonstrate that people's evaluation of the argument is sensitive to probabilistic factors deemed relevant on a Bayesian formalisation. Moreover, we provide the first parameter-free quantitative evidence in favour of the Bayesian approach to argumentation. Quantitative Bayesian prescriptions were derived from participants' stated subjective probabilities (Experiments 1 and 2), as well as from frequency information explicitly provided in the experiment (Experiment 3). Participants' stated evaluations of the convincingness of the argument were well matched to these prescriptions.