Event cameras capture scene changes asynchronously on a per-pixel basis, enabling extremely high temporal resolution. However, this advantage comes at the cost of high bandwidth, memory, and computational demands. To address this, prior work has explored event downsampling, but most approaches rely on fixed heuristics or threshold-based strategies, limiting their adaptability. Instead, we propose a probabilistic framework, POLED, that models event importance through an event-importance probability density function (ePDF), which can be arbitrarily defined and adapted to different applications. Our approach operates in a purely online setting, estimating event importance on-the-fly from raw event streams, enabling scene-specific adaptation. Additionally, we introduce zero-shot event downsampling, where downsampled events must remain usable for models trained on the original event stream, without task-specific adaptation. We design a contour-preserving ePDF that prioritizes structurally important events and evaluate our method across four datasets and tasks--object classification, image interpolation, surface normal estimation, and object detection--demonstrating that intelligent sampling is crucial for maintaining performance under event-budget constraints. Code available.