Autonomous Valet Parking (AVP) requires planning under partial observability, where parking spot availability evolves as dynamic agents enter and exit spots. Existing approaches either rely only on instantaneous spot availability or make static assumptions, thereby limiting foresight and adaptability. We propose an approach that estimates probability of future spot occupancy by distinguishing initially vacant and occupied spots while leveraging nearby dynamic agent motion. We propose a probabilistic estimator that integrates partial, noisy observations from a limited Field-of-View, with the evolving uncertainty of unobserved spots. Coupled with the estimator, we design a strategy planner that balances goal-directed parking maneuvers with exploratory navigation based on information gain, and incorporates wait-and-go behaviors at promising spots. Through randomized simulations emulating large parking lots, we demonstrate that our framework significantly improves parking efficiency and trajectory smoothness over existing approaches, while maintaining safety margins.