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Interactive 3D segmentation has emerged as a promising solution for generating accurate object masks in complex 3D scenes by incorporating user-provided clicks. However, two critical challenges remain underexplored: (1) effectively generalizing from sparse user clicks to produce accurate segmentations and (2) quantifying predictive uncertainty to help users identify unreliable regions. In this work, we propose \emph{NPISeg3D}, a novel probabilistic framework that builds upon Neural Processes (NPs) to address these challenges. Specifically, NPISeg3D introduces a hierarchical latent variable structure with scene-specific and object-specific latent variables to enhance few-shot generalization by capturing both global context and object-specific characteristics. Additionally, we design a probabilistic prototype modulator that adaptively modulates click prototypes with object-specific latent variables, improving the model’s ability to capture object-aware context and quantify predictive uncertainty. Experiments on four 3D point cloud datasets demonstrate that NPISeg3D achieves superior segmentation performance with fewer clicks while providing reliable uncertainty estimations.