This study focuses on people who have prostate cancer and are planning to have a radical prostatectomy (removal of prostate and some surrounding tissue). The purpose of the study is to assess the safety, tolerability, and feasibility of using epigenetic therapy, azacitidine, before planned radical prostatectomy to determine whether it increases the sensitivity of the tumor to the patient’s immune system. Epigenetic therapy uses specially designed drugs (such as azacitidine) to reprogram cancer cells back to a normal, noncancerous state. Researchers also want to know whether the therapy will lower the chance that the cancer returns and how well the body responds to the treatment. The study will collect and analyze participants’ surgical tumor tissue after they receive epigenetic therapy to look for changes in immune system activity. The use of azacitidine in this study is considered experimental.