In this study, we propose a new probabilistic hazard quantification strategy to provide the probability of Volcanic Ballistic Projectiles (VBPs) to exceed some critical kinetic energy thresholds, considering a variability on the site of the eruptive vents and the effect of wind. La Soufrière de Guadeloupe (Lesser Antilles) is chosen as a test case, focussing on the most likely explosive scenario associated with the eruption of an active lava dome (including phreatic, Vulcanian and Strombolian eruptions). Sensitivity analyses have guided the optimization of input parameters to balance the results stability and computational costs, showing that the topography is a pivotal factor when accounting for the spatial uncertainty on vent locations in the proximity of the dome area. Given an eruption within the adopted scenario, we provide maps showing the probability to exceed different energy reference thresholds for roof's perforation if at least one VBP falls in a target area. These maps are then combined with exposed elements to produce a qualitative exposure-based risk map. We compute the overall probability, conditional on the selected scenario, for roof perforation in a given area when a VBP is ejected. Results show probabilities varying from ca. 2% up to 40% within a few km from the volcano, quickly dropping away from the dome. However, when the probability to exceed the energy reference threshold is only conditional on falling of VBPs in a target area, most of Basse-Terre island would be affected by the 20-60% probability of roof perforation. This work confirms how the choice of a probabilistic approach is key to estimate the likelihood of occurrence of VBPs impacts as a first step towards the development and implementation of pro-active risk reduction strategies in volcanic areas.