In this paper, a diffusion-based molecular communication channel is modeled in presence of a probabilistic absorber. The probabilistic absorber is an absorber which absorbs molecules upon collision with probability q . With random walk analysis, the discrete probability function of particle location in the presence of a probabilistic absorber can be found. Then, a continuous probability function is fitted to this Markov-based results with introducing several fitting parameters to the known probability function of particle location in an unbounded environment without an absorbing barrier. With this approach, a single receptor is modeled as an M/M/1/1 queue in which q represents the complementary blocking probability and the mean service time is the mean trafficking time. Therefore, we are able to model the stochastic nature of ligand-receptor binding, which comes from the incapability of a receptor to receive all molecules in its space; and also known as receptor occupancy. The proper consideration of the absorption effect leads to the accurate calculation of the concentration at the desired site, which is definitely less than the concentration obtained when neglecting it. These findings can have a crucial role in designing drug delivery systems in which determining the optimal rate of the drug transmitting nanomachines is critical to avoid toxicity while maintaining effectiveness.