Machine-learning frameworks such as Bayesian networks are widely acknowledged for their capability to reason under uncertainty. However their massive computational requirement, when implemented on conventional computers, hinders their usefulness in critical problem areas. We propose a non von Neumann machine paradigm purposefully architected with physical equivalence across all layers for solving these problems efficiently. It uses emerging magneto-electric nanoscale devices in a novel mixed-signal circuit framework operating directly on probabilities, without segregation between memory and computation. Based on bottom-up simulations, we show four orders of magnitude performance improvement vs. best-of-breed microprocessors with 100 cores, for Bayesian inference involving a million variables. Smaller problem sizes in the order of a 100 variables can be realized at 12mW power consumption and very low area of about a tenth of a mm². Our vision is to enable solving complex Bayesian problems in real time, while incorporating intelligence capabilities at smaller scales everywhere.