Downsampling images and labels, often necessitated by limited resources or to expedite network training, leads to the loss of small objects and thin boundaries. This undermines the segmentation network's capacity to interpret images accurately and predict detailed labels, resulting in diminished performance compared to processing at original resolutions. This situation exemplifies the trade-off between efficiency and accuracy, with higher downsampling factors further impairing segmentation outcomes. Preserving information during downsampling is especially critical for medical image segmentation tasks. To tackle this challenge, we introduce a novel method named Edge-preserving Probabilistic Downsampling (EPD). It utilizes class uncertainty within a local window to produce soft labels, with the window size dictating the downsampling factor. This enables a network to produce quality predictions at low resolutions. Beyond preserving edge details more effectively than conventional nearest-neighbor downsampling, employing a similar algorithm for images, it surpasses bilinear interpolation in image downsampling, enhancing overall performance. Our method significantly improved Intersection over Union (IoU) to 2.85%, 8.65%, and 11.89% when downsampling data to 1/2, 1/4, and 1/8, respectively, compared to conventional interpolation methods.