Described is a system for computing conditional probabilities of random variables for Bayesian inference. The system implements a spiking neural network of neurons to compute the conditional probability of two random variables X and Y. The spiking neural network includes an increment path for a synaptic weight that is proportional to a product of the synaptic weight and a probability of X, a decrement path for the synaptic weight that is proportional to a probability of X, Y, and delay and spike timing dependent plasticity (STDP) parameters such that the synaptic weight increases and decreases with the same magnitude for a single firing event.