§ 121. Private ownership or operation of correctional facilities. Except as otherwise provided in subdivisions two, three and four of section one hundred twenty of this article or in federal law, the private operation or management of a correctional facility as defined in subdivision four of section two of this chapter or a local correctional facility, as defined in subdivision sixteen of section two of this chapter, the private ownership or operation of a facility for housing state or local inmates or the private ownership or operation of a facility for the incarceration of other state's inmates is prohibited.