The automated analysis of medical time series, such as the electrocardiogram (ECG), electroencephalogram (EEG), pulse oximetry, etc, has the potential to serve as a valuable tool for diagnostic decisions, allowing for remote monitoring of patients and more efficient use of expensive and time-consuming medical procedures. Deep neural networks (DNNs) have been demonstrated to process such signals effectively. However, previous research has primarily focused on classifying medical time series rather than attempting to regress the continuousvalued physiological parameters central to diagnosis. One significant challenge in this regard is the imbalanced nature of the dataset, as a low prevalence of abnormal conditions can lead to heavily skewed data that results in inaccurate predictions and a lack of certainty in such predictions when deployed. To address these challenges, we propose HypUC, a framework for imbalanced probabilistic regression in medical time series, making several contributions. (i) We introduce a simple kernel density-based technique to tackle the imbalanced regression problem with medical time series. (ii) Moreover, we employ a probabilistic regression framework that allows uncertainty estimation for the predicted continuous values. (iii) We also present a new approach to calibrate the predicted uncertainty further. (iv) Finally, we demonstrate a technique to use calibrated uncertainty estimates to improve the predicted continuous value and show the efficacy of the calibrated uncertainty estimates to flag unreliable predictions. HypUC is evaluated on a large, diverse, real-world dataset of ECGs collected from millions of patients, outperforming several conventional baselines on various diagnostic tasks, suggesting potential use-case for the reliable clinical deployment of deep learning models and a prospective clinical trial. Consequently, a hyperkalemia diagnosis algorithm based on HypUC is going to be the subject of a real-world clinical prospective study.