Advanced Air Mobility (AAM) is a growing field that demands accurate and trustworthy models of legal concepts and restrictions for navigating Unmanned Aircraft Systems (UAS). In addition, any implementation of AAM needs to face the challenges posed by inherently dynamic and uncertain human-inhabited spaces robustly. Nevertheless, the employment of UAS beyond visual line of sight (BVLOS) is an endearing task that promises to significantly enhance today's logistics and emergency response capabilities. Hence, we propose Probabilistic Mission Design (ProMis), a novel neuro-symbolic approach to navigating UAS within legal frameworks. ProMis is an interpretable and adaptable system architecture that links uncertain geospatial data and noisy perception with declarative, Hybrid Probabilistic Logic Programs (HPLP) to reason over the agent's state space and its legality. To inform planning with legal restrictions and uncertainty in mind, ProMis yields Probabilistic Mission Landscapes (PML). These scalar fields quantify the belief that the HPLP is satisfied across the agent's state space. Extending prior work on ProMis' reasoning capabilities and computational characteristics, we show its integration with potent machine learning models such as Large Language Models (LLM) and Transformer-based vision models. Hence, our experiments underpin the application of ProMis with multi-modal input data and how our method applies to many AAM scenarios.