In moving object environments it is infeasible for the database tracking the movement of objects to store the exact locations of objects at all times. Typically the location of an object is known with certainty only at the time of the update. The uncertainty in its location increases until the next update. In this environment, it is possible for queries to produce incorrect results based upon old data. However, if the degree of uncertainty is controlled, then the error of the answers to certain queries can be reduced. More generally, query answers can be augmented with probabilistic estimates of the validity of the answer. In this paper we study the execution of such probabilistic nearest-neighbor queries. The imprecision in answers to the queries is an inherent property of these applications due to uncertainty in the data, unlike the techniques for approximate nearest-neighbor processing that trade accuracy for performance.