This paper presents a probabilistic impedance-based fault location method (FLM) designed for medium voltage (MV) distribution feeders using zero-sequence (ZS) components with few additional voltage measurements on secondary substations. It is based on a previous work in which a novel FLM has been developed and showed promising locating performance on the most challenging ramified rural feeders. However, this method has been found to be too sensitive to measurement errors to be deployable with the current generation of sensors. Thus, this paper presents a probabilistic formulation of the fault location problem with Monte-Carlo simulations which fits two four-dimensional Gaussian probability density functions (PDFs) of the ZS voltage and current on the considered paths (between the busbar and each measurement node) on a MV feeder. This way, our fault location algorithm is robust to both measurement and line impedance errors. A criterion for the optimal number of Monte-Carlo simulations as well as an efficient way to compute the similarity between two different PDFs in several dimensions are proposed. Finally, it is shown that the performances of this algorithm are highly correlated to the value of the threshold probability.