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Databases enable users to precisely express their informational needs using structured queries. However, database query construction is a laborious and error-prone process, which cannot be performed well by most end users. Keyword search alleviates the usability problem at the price of query expressiveness. As keyword search algorithms do not differentiate between the possible informational needs represented by a keyword query, users may not receive adequate results. This paper presents IQP - a novel approach to bridge the gap between usability of keyword search and expressiveness of database queries. IQP enables a user to start with an arbitrary keyword query and incrementally refine it into a structured query through an interactive interface. The enabling techniques of IQP include: 1) a probabilistic framework for incremental query construction; 2) a probabilistic model to assess the possible informational needs represented by a keyword query; 3) an algorithm to obtain the optimal query construction process. This paper presents the detailed design of IQP, and demonstrates its effectiveness and scalability through experiments over real-world data and a user study.