Probability distribution of the node degree has long been regarded as one of the important metrics to characterize the wireless ad hoc networks. However, there is no exact formulation for this probability distribution when shadow fading effects are considered. In this letter, by deriving the conditional probability of the node degree and the joint distribution of the distances between nodes and a randomly selected reference node (RSRN), we show that the probability distribution of the node degree for the wireless ad hoc networks in the shadow fading environments is binomial.