Stochastic multicomponent reactive transport modeling is a powerful approach to quantify the probability of non-exceedance (PNE) of arsenic (As) critical concentration thresholds in groundwater. The approach is applied to a well-characterized shallow alluvial aquifer near Venice, Italy. Here, As mobility depends primarily on rainfall-controlled redox-dependent precipitation-dissolution of iron hydroxides. A Monte-Carlo analysis based on a calibrated three-dimensional flow and transport model targeted the geochemical initial conditions as the main source of uncertainty of As concentrations in the studied aquifer. It was found that, during 115 simulated days, the fraction of the entire aquifer volume with As > 10 μgL−1 decreased on average from ~43% to ~39% and the average As concentration from ~32 μgL−1 to ~27 μgL−1. Meanwhile, PNE increased from 55% to 60% when 10 μgL−1 was set as target threshold, and from 71% to 78% for 50 μgL−1. The time dependence of As attenuation can be ascribed to the increase of oxidizing conditions during rainfall-dependent aquifer recharge, which causes As sorption on precipitating iron hydroxides. When computing the same statistics for the shallowest 6 m, As attenuation was even more evident. The volume fraction of aquifer with As > 10μgL−1 dropped from 40% to 28% and the average As concentration from 31 μgL−1 to 20 μgL−1, whereas PNE increased from 58% to 70% for As < 10 μgL−1 and from 71% to 86% for As < 50 μgL−1. Thus, the wells screen depth in the aquifer can be a critical aspect when estimating As risk, owing to the depth-dependent relative change in redox conditions during rainfall events.