In this article, we present an original neural space/latency code, integrated in a multi-layered neural hierarchy, that offers a new perspective on probabilistic inference operations. Our work is based on the dynamic neural field paradigm that leads to the emergence of activity bumps, based on recurrent lateral interactions, thus providing a spatial coding of information. We propose that lateral connections represent a data model, i.e., the conditional probability of a "true" stimulus given a noisy input. We propose furthermore that the resulting attractor state encodes the most likely "true" stimulus given the data model, and that its latency expresses the confidence in this interpretation. Thus, the main feature of this network is its ability to represent, transmit and integrate probabilistic information at multiple levels so that to take near-optimal decisions when inputs are contradictory, noisy or missing. We illustrate these properties on a three-layered neural hierarchy receiving inputs from a simplified robotic object recognition task. We also compare the network dynamics to an explicit probabilistic model of the task, to verify that it indeed reproduces all relevant properties of probabilistic processing.