Elastic Optical Networks (EONs) enable optical circuits to be assigned distinct numbers of spectrum slices. Individual circuits can then be assigned an optimal number of slices to best match their target transmission rates. A well-known drawback of EONs is spectrum fragmentation and its resulting uneven blocking probability, which circuit requests experience when the available spectrum slices in the fiber are insufficient or not contiguous. Capturing this spectrum fragmentation problem analytically is a challenging problem. Not surprisingly, most of the existing studies at this time mainly use simulation-based techniques to quantify blocking probability in EONs. In this paper, the authors present a Markov Chain (MC) model that attempts to characterize the fragmentation problem in a simplified scenario, i.e., only two types of circuit services are allowed over a single fiber link. Despite its limited scope, this initial analytical effort is able to accurately capture the non-monotonic behavior of the blocking probability in EONs for the first time.