Decision-making in the area of coastal adaptation is facing major challenges due to ambiguity (i.e., deep uncertainty) pertaining to the selection of a probability model for sea level rise (SLR) projections. Possibility distributions are mathematical tools that address this type of uncertainty since they bound all the plausible probability models that are consistent with the available data. In the present study, SLR uncertainties are represented by a possibility distribution constrained by likely ranges provided in the IPCC Fifth Assessment Report and by a review of high-end scenarios. On this basis, we propose a framework combining probabilities and possibilities to evaluate how SLR uncertainties accumulate with other sources of uncertainties, such as future greenhouse gas emissions, upper bounds of future sea level changes, the regional variability of sea level changes, the vertical ground motion, and the contributions of extremes and wave effects. We apply the framework to evaluate the probability of coastal flooding by the year 2100 at a local, low-lying coastal French urban area on the Mediterranean coast. We show that when adaptation is limited to maintaining current defenses, the level of ambiguity is too large to precisely assign a probability model to future flooding. Raising the coastal walls by 85cm creates a safety margin that may not be considered sufficient by local stakeholders. A sensitivity analysis highlights the key role of deep uncertainties pertaining to global SLR and of the statistical uncertainty related to extremes. The ranking of uncertainties strongly depends on the decision-maker's attitude to risk (e.g., neutral, averse), which highlights the need for research combining advanced mathematical theories of uncertainties with decision analytics and social science.