We describe an adaptive and parameter-free density estimator that provides an accurate measure of the probability and of its uncertainty for non-uniform samples embedded in high dimensional spaces. The estimator uses only distances between the points and not the coordinates and does not require any assumption on the functional form of the probability distribution. We discuss its accuracy on artificial data sets including probability values spanning many orders of magnitude. The availability of an error estimate allows distinguishing genuine density peaks from statistical fluctuations due to finite sampling. This is an essential ingredient for robustly inferring the topography of the probability distributions, namely for finding the location and height of the density peaks and of the saddles between them.