Abstract: According to the Probability Ranking Principle (PRP), ranking documents in decreasing order of their probability of relevance leads to an optimal document ranking for ad-hoc retrieval. The PRP holds when two conditions are met: [C1] the models are well calibrated, and, [C2] the probabilities of relevance are reported with certainty. We know however that deep neural networks (DNNs) are often not well calibrated and have several sources of uncertainty, and thus [C1] and [C2] might not be satisfied by neural rankers. Given the success of neural Learning to Rank (LTR) approaches---and here, especially BERT-based approaches---we first analyze under which circumstances deterministic neural rankers are calibrated for conversational search problems. Then, motivated by our findings we use two techniques to model the uncertainty of neural rankers leading to the proposed stochastic rankers, which output a predictive distribution of relevance as opposed to point estimates. Our experimental results on the ad-hoc retrieval task of conversation response ranking reveal that (i) BERT-based rankers are not robustly calibrated and that stochastic BERT-based rankers yield better calibration; and (ii) uncertainty estimation is beneficial for both risk-aware neural ranking, i.e. taking into account the uncertainty when ranking documents, and for predicting unanswerable conversational contexts.