Spiking neural networks (SNN) are promising artificial neural network (ANN) models as they utilise information representation as trains of spikes, that adds new dimensions of time, frequency and phase to the structure and the functionality of ANN. The current SNN models though are deterministic, that restricts their applications for large scale engineering and cognitive modelling of stochastic processes. This paper proposes a novel probabilistic spiking neuron model (pSNM) and suggests ways of building pSNN for a wide range of applications including classification, string pattern recognition and associative memory. It also extends previously published computational neurogenetic models.