Neural Radiance Fields (NeRF) have advanced photorealistic novel view synthesis, but their reliance on photometric reconstruction introduces artifacts, commonly known as "floaters". These artifacts degrade novel view quality, especially in areas unseen by the training cameras. We present a fast, post-hoc NeRF cleanup method that eliminates such artifacts by enforcing our Free Space Prior, effectively minimizing floaters without disrupting the NeRF's representation of observed regions. Unlike existing approaches that rely on either Maximum Likelihood (ML) estimation to fit the data or a complex, local data-driven prior, our method adopts a Maximum-a-Posteriori (MAP) approach, selecting the optimal model parameters under a simple global prior assumption that unseen regions should remain empty. This enables our method to clean artifacts in both seen and unseen areas, enhancing novel view quality even in challenging scene regions. Our method is comparable with existing NeRF cleanup models while being 2.5x faster in inference time, requires no additional memory beyond the original NeRF, and achieves cleanup training in less than 30 seconds. Our code will be made publically available.