Probabilistic inference over large data sets is a challenging data management problem since exact inference is generally #P-hard and is most often solved approximately with sampling-based methods today. This paper proposes an alternative approach for approximate evaluation of conjunctive queries with standard relational databases: In our approach, every query is evaluated entirely in the database engine by evaluating a fixed number of query plans, each providing an upper bound on the true probability, then taking their minimum. We provide an algorithm that takes into account important schema information to enumerate only the minimal necessary plans among all possible plans. Importantly, this algorithm is a strict generalization of all known PTIME self-join-free conjunctive queries: A query is in PTIME if and only if our algorithm returns one single plan. Furthermore, our approach is a generalization of a family of efficient ranking methods from graphs to hypergraphs. We also adapt three relational query optimization techniques to evaluate all necessary plans very fast. We give a detailed experimental evaluation of our approach and, in the process, provide a new way of thinking about the value of probabilistic methods over non-probabilistic methods for ranking query answers. We also note that the techniques developed in this paper apply immediately to lifted inference from statistical relational models since lifted inference corresponds to PTIME plans in probabilistic databases.