The goal of combining the robustness of neural networks and the expressivity of symbolic methods has rekindled the interest in Neuro-Symbolic AI. One specifically interesting branch of research is deep probabilistic programming languages (DPPLs) which carry out probabilistic logical programming via the probability estimations of deep neural networks. However, recent SOTA DPPL approaches allow only for limited conditional probabilistic queries and do not offer the power of true joint probability estimation. In our work, we propose an easy integration of tractable probabilistic inference within a DPPL. To this end we introduce SLASH, a novel DPPL that consists of Neural-Probabilistic Predicates (NPPs) and a logical program, united via answer set programming. NPPs are a novel design principle allowing for the unification of all deep model types and combinations thereof to be represented as a single probabilistic predicate. In this context, we introduce a novel $+/-$ notation for answering various types of probabilistic queries by adjusting the atom notations of a predicate. We evaluate SLASH on the benchmark task of MNIST addition as well as novel tasks for DPPLs such as missing data prediction, generative learning and set prediction with state-of-the-art performance, thereby showing the effectiveness and generality of our method.