Predicting and describing probabilistically the behavior of traffic participants is crucial for improving the trajectory planning of vehicles in critical traffic scenarios. A deep learning architecture is introduced in this work to predict a probabilistic space-time representation of the future, termed as the predicted Occupancy Grid Map (predicted OGM), that includes the interaction between the traffic participants as well as the uncertainties regarding their motion behavior. The architecture is based on Variational AutoEncoders (VAEs) and Random Forests (RFs) and it is introduced to obtain fine time step resolutions of the predicted OGMs that are required to plan a safe trajectory. The structure in the latent space of the VAEs is explored to enable the semantic manipulation of data. The VAEs are used for two purposes in this paper. One is to compress the input into a low dimensional space and the other is to sample in the latent space thereby generating realistic samples of the predicted OGMs. The proposed model is validated based on the publicly available highD dataset. The results demonstrate the effectiveness of the proposed method. Also, the possibility to use the predicted OGMs for safe trajectory planning of the ego vehicle is demonstrated.