Currently, most reliable and commercialized artificial pancreas systems for type 1 diabetes are hybrid closed-loop systems, which require the user to announce every meal and its size. However, estimating the amount of carbohydrates in a meal and announcing each and every meal is an error-prone process that introduces important uncertainties to the problem, which when not considered, lead to sub-optimal outcomes of the controller. To address this problem, we propose a novel deep-learning-based model for probabilistic glucose prediction, called the Input and State Recurrent Kalman Network (ISRKN), which consists in the incorporation of an input and state Kalman filter in the latent space of a deep neural network so that the posterior distributions can be computed in closed form and the uncertainty can be propagated using the Kalman equations. In addition, the proposed architecture allows explicit estimation of the meal uncertainty distribution, whose parameters are encoded in the filter parameters. Results using the UVA/Padova simulator and data from a clinical trial show that the proposed model outperforms other probabilistic models using several probabilistic metrics across different degrees of distributional shifts.