Reconstructing semantic 3D building models at the level of detail (LoD) 3 is a long-standing challenge. Unlike mesh-based models, they require watertight geometry and object-wise semantics at the fa\c{c}ade level. The principal challenge of such demanding semantic 3D reconstruction is reliable fa\c{c}ade-level semantic segmentation of 3D input data. We present a novel method, called Scan2LoD3, that accurately reconstructs semantic LoD3 building models by improving fa\c{c}ade-level semantic 3D segmentation. To this end, we leverage laser physics and 3D building model priors to probabilistically identify model conflicts. These probabilistic physical conflicts propose locations of model openings: Their final semantics and shapes are inferred in a Bayesian network fusing multimodal probabilistic maps of conflicts, 3D point clouds, and 2D images. To fulfill demanding LoD3 requirements, we use the estimated shapes to cut openings in 3D building priors and fit semantic 3D objects from a library of fa\c{c}ade objects. Extensive experiments on the TUM city campus datasets demonstrate the superior performance of the proposed Scan2LoD3 over the state-of-the-art methods in fa\c{c}ade-level detection, semantic segmentation, and LoD3 building model reconstruction. We believe our method can foster the development of probability-driven semantic 3D reconstruction at LoD3 since not only the high-definition reconstruction but also reconstruction confidence becomes pivotal for various applications such as autonomous driving and urban simulations.