ProBoost, a new boosting algorithm for probabilistic classifiers, is proposed in this work. This algorithm uses the epistemic uncertainty of each training sample to determine the most challenging/uncertain ones; the relevance of these samples is then increased for the next weak learner, producing a sequence that progressively focuses on the samples found to have the highest uncertainty. In the end, the weak learners' outputs are combined into a weighted ensemble of classifiers. Three methods are proposed to manipulate the training set: undersampling, oversampling, and weighting the training samples according to the uncertainty estimated by the weak learners. Furthermore, two approaches are studied regarding the ensemble combination. The weak learner herein considered is a standard convolutional neural network, and the probabilistic models underlying the uncertainty estimation use either variational inference or Monte Carlo dropout. The experimental evaluation carried out on MNIST benchmark datasets shows that ProBoost yields a significant performance improvement. The results are further highlighted by assessing the relative achievable improvement, a metric proposed in this work, which shows that a model with only four weak learners leads to an improvement exceeding 12% in this metric (for either accuracy, sensitivity, or specificity), in comparison to the model learned without ProBoost.