The scalability and non-ideality issues of the memristor circuits poses several challenges to the implementation of analog memristive probabilistic neural networks in hardware. To meet the emerging challenges of faster edge AI computing devices, the integration of neural networks within or near to the sensor can improve the data processing times, reduce bandwidth requirements, and reduce data transfer errors. The fast learning in probabilistic neural network (PNN) make it an attractive solution for energy efficient computing in edge devices. The PNN estimates the density function of the categories and classifies the input based on the Bayes decision rule. It avoids backpropagation, since weights are derived from training samples directly and set in the first initialization stage. The proposed hardware realization of the PNN is based on a memristor crosssbar architecture. The simulations demonstrate that the accuracy of the hardware realization of the PNN can be as high as 93.3% for the MNIST dataset if a proper smoothing parameter is selected.