Nivolumab + Docetaxel + ADT in mHSPC Patients With DDRD or Inflamed Tumors

This research study is studying a combination of hormonal therapy, chemotherapy, and immunotherapy as a possible treatment for metastatic hormone-sensitive prostate cancer. The names of the study drugs involved in this study are: * Androgen deprivation therapy (ADT) with a drug of your physician's choice. This may include leuprolide (Lupron), goserelin acetate (Zoladex), or degarelix (Firmagon). * Docetaxel * Nivolumab

Inclusion Criteria: * Newly diagnosed histologically confirmed prostate adenocarcinoma within 6 months prior to study registration with evidence of high-volume distant metastasis on conventional imaging * Distant metastasis is defined by non-regional lymph node(s) metastasis (M1a), bone metastasis (M1b), and/or other site(s) of metastatic disease (M1c). * Conventional imaging consists of CT, MRI or radionuclide bone scan * High volume of disease is defined by presence of four or more bone lesions with at least one beyond the vertebral bodies or pelvis or any site of visceral metastasis. * Age ≥18 years * ECOG performance status ≤2 (Karnofsky ≥60%, see Appendix A) * Subjects with ECOG performance status of 2 are only eligible if the performance status decline is attributed to metastatic prostate cancer * Serum PSA \> 4.0 ng/mL before initiation of ADT * Serum testosterone \> 100 ng/dL before initiation of ADT * Subjects whose testosterone level is unknown before initiation of ADT may be allowed after discussion with Sponsor-Investigator. * Grade ≤ 1 peripheral neuropathy, defined as asymptomatic or paresthesia and/or decreased deep tendon reflexes is allowed. * Subjects must have adequate organ and marrow function as defined below: * Absolute neutrophil count ≥1,500 /mcL * Platelets ≥100,000 /mcL * Total bilirubin ≤1.5 × institutional upper limit of normal. Exception: Subjects with confirmed Gilbert's syndrome (persistent or recurrent hyperbilirubinemia that is predominantly unconjugated in the absence of hemolysis or hepatic pathology) may be allowed after consultation with treating physician * AST(SGOT) and ALT(SGPT) ≤2.5 × institutional upper limit of normal. Exception: ≤5 x institutional upper limit of normal in subjects with liver metastasis * Creatinine (Cr) and creatinine clearance (CrCl) Cr \