This paper is an upgrade of a previous work on an impedance-based fault location method (FLM) designed for medium voltage (MV) distribution feeders using zerosequence (ZS) components and distributed voltage measurements [1]. This paper proposes to estimate ZS voltage probability density functions (PDFs) instead of amplitude and phase. Indeed, impedance-based FLMs are sensitive to measurement errors as well as line impedance value uncertainties, which tend to be higher at the distribution level. Thus, this paper presents a probabilistic formulation for fault location which is robust to both measurement and line impedance values errors with as few as possible additional voltage measurements needed on some secondary substations. A series of Monte-Carlo simulations enable us to fit two 4-dimensional Gaussian PDFs for ZS current and voltage and perform robust fault location by computing the volume inside the intersection of the two 2-dimensional marginal voltage PDFs estimated along a path of nodes on the feeder. This probabilistic formulation comes at the expense of an increase in the size of the fault location area with respect to the previous formulation. However, in most cases, this formulation offers a high increase in robustness while leading to a minor diminution of locating precision. The proposed algorithm has been validated with simulated faults on the CIGRE MV benchmark network (CIGRE network).