We propose techniques for exploratory search in large databases. The goal is to provide new functionality that aids users in homing in on the right query conditions to find what they are looking for. Query refinement proceeds interactively by repeatedly consulting the user to manage query conditions. This process is characterized by three key challenges: (1) dealing with incomplete and imprecise user input, (2) keeping user effort low, and (3) guaranteeing interactive system response time. We address the first two challenges with a probability-based framework that guides the user to the most important query conditions. To recover from input errors, we introduce the notion of sensitivity and propose efficient algorithms for identifying the most sensitive user input, i.e., those inputs that had the greatest influence on the query results. For the third challenge, we develop techniques that can deliver estimates of the required probabilities within a given hard realtime limit and are able to adapt automatically as the interactive query refinement proceeds.