This paper presents a novel method for ground segmentation. Terrain analysis is of paramount importance for the safe navigation of autonomous robots. In this study, we introduce GATA, a probabilistic real-time graph-based method for segmentation and traversability analysis of point clouds. In the method, we iteratively refine the parameters of a ground plane model and identify regions imaged by a LiDAR as traversable and non-traversable. The method excels in delivering rapid, high-precision obstacle detection, surpassing existing state-of-the-art methods. Furthermore, our method addresses the need to distinguish between surfaces with varying traversability, such as vegetation or unpaved roads, depending on the specific application. To achieve this, we integrate a shallow neural network, which operates on features extracted from the ground model. This enhancement not only boosts performance but also maintains real-time efficiency, without the need for GPUs. The method is rigorously evaluated using the SemanticKitti dataset and its practicality is showcased through real-world experiments with an urban last-mile delivery autonomous robot. The code is publicly available at https://gitlab.iri.upc.edu/idelpino/iri_ground_segmentation.