In database-driven opportunistic spectrum access, location information of secondary users plays an important role. In a database query-and-update procedure, a secondary user reports to the geolocation database of its location information, so that the updated knowledgebase facilitates location-aided incumbent protection and network coexistence. However, such database-driven spectrum sharing becomes very challenging when the secondary users are mobile. In this paper, we propose a probabilistic coexistence framework that supports mobile users by incorporating the solutions to solve two core problems: (i) white space allocation (WSA) at the database and (ii) location update control (LUC) at the users. We frame the two problems such that they interact through dynamic control of the users' location uncertainty levels. For WSA, we derive a centralized real-time solution to mitigate mutual interference among secondary users and protect primary users against harmful interference. For LUC, we design a local two-level strategy to enable both movement-driven and interference-driven control of location uncertainty. This strategy makes an appropriate trade-off between the effectiveness of interference mitigation and the cost of database queries. To evaluate our algorithms, we have carried out both theoretical model-driven and real-world trace-driven simulation experiments. Our simulation results show that the proposed framework can determine and adapt the database query intervals of mobile users to achieve near-optimal interference mitigation with minimal location updates.