Inclusion Criteria: - Histologic confirmation of adenocarcinoma of the prostate without small cell features - Current evidence of metastatic disease documented by either bone lesions on radionuclide bone scan and/or soft tissue lesions on computerized tomography/magnetic resonance imaging (CT/MRI) - Eastern Cooperative Oncology Group (ECOG) performance status 0-1 - Ongoing androgen deprivation therapy (ADT) with a gonadotropin-releasing hormone (GnRH) analogue or bilateral orchiectomy - Documented prostate cancer progression per Prostate Cancer Working Group (PCWG3) criteria within 6 months prior to screening - Chemotherapy-naïve for metastatic castration-resistant prostate cancer (mCRPC), with 1 to 2 prior second generation hormonal therapies in the recurrent non-metastatic setting and/or metastatic setting, and no more than 1 second generation hormonal therapy in the mCRPC setting. Must have progressed during or after second generation hormonal therapy or have documented intolerance to second generation hormonal therapy - Participants must meet one of the following criteria regarding tissue submission: Sufficient tumor samples from a newly obtained ("fresh") biopsy (obtained during screening); or archival tumor tissue in the form of formalin-fixed paraffin-embedded (FFPE) block or unstained tumor tissue slides. For participants with bone-only disease or inaccessible soft tissue lesions or if the biopsy procedure would pose an unacceptable clinical risk for the participant, submission of tumor tissue obtained from a fresh biopsy is not required. - Men must agree to follow specific methods of contraception, if applicable Exclusion Criteria: - Active brain metastases - Active, known, or suspected autoimmune disease - Condition requiring systemic treatment with corticosteroids (> 10 mg daily prednisone equivalent) or other immunosuppressive medications within 14 days of start of study treatment. Inhaled or topical steroids or adrenal replacement steroid doses are permitted in the absence of active autoimmune disease - Prior treatment with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CTLA-4 antibody, or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways - Prior treatment with docetaxel or other chemotherapy for mCRPC. Prior docetaxel for metastatic castration-sensitive prostate cancer is permitted if at least 12 months have elapsed from last dose of docetaxel Other protocol-defined inclusion/exclusion criteria apply