The human capacity for causal judgment has long been thought to depend on an ability to consider counterfactual alternatives: the lightning strike caused the forest fire because had it not struck, the forest fire would not have ensued. To accommodate psychological effects on causal judgment, a range of recent accounts of causal judgment have proposed that people probabilistically sample counterfactual alternatives from which they compute a graded index of causal strength. While such models have had success in describing the influence of probability on causal judgments, among other effects, we show that these models make further untested predictions: probability should also influence people's metacognitive confidence in their causal judgments. In a large (N=3020) sample of participants in a causal judgment task, we found evidence that normality indeed influences people's confidence in their causal judgments and that these influences were predicted by a counterfactual sampling model. We take this result as supporting evidence for existing Bayesian accounts of causal judgment.