Information extraction and human collaboration techniques are widely applied in the construction of web-scale knowledge bases. However, these knowledge bases are often incomplete or uncertain. In this paper, we present ProbKB, a probabilistic knowledge base designed to infer missing facts in a scalable, probabilistic, and principled manner using a relational DBMS. The novel contributions we make to achieve scalability and high quality are: 1) We present a formal definition and a novel relational model for probabilistic knowledge bases. This model allows an efficient SQL-based inference algorithm for knowledge expansion that applies inference rules in batches; 2) We implement ProbKB on massive parallel processing databases to achieve further scalability; and 3) We combine several quality control methods that identify erroneous rules, facts, and ambiguous entities to improve the precision of inferred facts. Our experiments show that ProbKB system outperforms the state-of-the-art inference engine in terms of both performance and quality.