Active visual exploration of tabletop objects often requires reorienting an unknown resting object onto a different stable support face to expose occluded surfaces. To identify such placements without exhaustive physical search, we learn a probabilistic placement prior from a single-view point cloud. Stable placement prediction is inherently multimodal, and conventional 6-DoF regression introduces further ambiguity by modeling translation and in-plane yaw. We therefore propose FlipToSee, a probabilistic framework that removes this representational ambiguity by parameterizing placements as unit support normals on S2 while modeling their multimodal conditional distribution via a von Mises--Fisher mixture density network. To decouple mode diversity from physical robustness, FlipToSee deterministically extracts a compact candidate set from the mixture components and applies robustness-aware reranking using an auxiliary head trained with candidate-aligned supervision. In simulation, FlipToSee achieves 98.4% first-proposal success on in-distribution objects, 95.3% on out-of-distribution shapes, and 90.0% under zero-shot transfer to household YCB objects. We further demonstrate the learned placement prior on a physical robot by integrating it with grasp and motion planning for exploratory regrasping.