In location-based services, it is common for a user to issue a query based on his/her current position. One such example is "find the available cabs within two miles of my current location". Very often, the query issuers' locations are imprecise due to measurement error, sampling error, or message delay. They may also want to protect their privacy by providing a less precise location. In this paper, we study the efficiency of queries that return probabilistic guarantees for location data with uncertainty. We classify this query into two types, based on whether the data (1) has no uncertainty (e.g., shops and restaurants), or (2) has a controlled degree of uncertainty (e.g., moving vehicles). Based on this classification, we develop three methods to improve the computational and I/O performance. The first method expands the query range based on the query issuer's uncertainty. The second idea exchanges the roles of query and data. The third technique exploits the fac...