Uncertainty quantification is an important topic for many environmental studies, such as identifying zones where potentially toxic materials exist in the soil. In this work, the nonparametric geostatistical framework of histogram via entropy reduction (HER) is adapted to address local and spatial uncertainty in the context of risk of soil contamination. HER works with empirical probability distributions, coupling information theory and probability aggregation methods to estimate conditional distributions, which gives it the flexibility to be tailored for different data and application purposes. To explore the method adaptation for handling estimations of threshold-exceeding probabilities, it is used to map the risk of soil contamination by lead in the well-known dataset of the region of Swiss Jura. Its results are compared to indicator kriging (IK) and to an ordinary kriging (OK) model available in literature. For the analyzed dataset, IK and HER achieved the best performance and exhibited comparable accuracy and precision of their predictions. When compared to IK, HER has shown to be a unique approach for dealing with uncertainty estimation in a fine resolution, without the need of modeling multiple indicator variograms, correcting order-relation violations, or defining interpolation/extrapolation of distribution. Finally, to avoid the well-known smoothing effect when using point estimations (this is the case with kriging, but also with HER) and to provide maps that reflect the spatial fluctuation of the revealed reality, we demonstrate how HER can be used in combination with sequential simulation to assess spatial uncertainty (uncertainty jointly over several locations).