Learning and perception from multiple sensory modalities are crucial processes for the development of intelligent systems capable of interacting with humans. We present an integrated probabilistic framework for perception, learning and memory in robotics. The core component of our framework is a computational Synthetic Autobiographical Memory model which uses Gaussian Processes as a foundation and mimics the functionalities of human memory. Our memory model, that operates via a principled Bayesian probabilistic framework, is capable of receiving and integrating data flows from multiple sensory modalities, which are combined to improve perception and understanding of the surrounding environment. To validate the model, we implemented our framework in the iCub humanoid robotic, which was able to learn and recognise human faces, arm movements and touch gestures through interaction with people. Results demonstrate the flexibility of our method to successfully integrate multiple sensory inputs, for accurate learning and recognition. Thus, our integrated probabilistic framework offers a promising core technology for robust intelligent systems, which are able to perceive, learn and interact with people and their environments.