The 1841 British edition accidentally added a the before prison, as if this prison had already been mentioned. The following LDS edition (1849) removed this intrusive the. As expected in English, the text generally refers to someone being “in prison” or being cast “into prison” unless events within a specific prison are being told. So when Alma and Amulek are cast into prison at Ammonihah (Alma 14:18–29), the narrative describes the events that occurred “in the prison”, similarly for Nephi and Lehi when they were in the prison at the city of Nephi-Lehi (Helaman 5:21–44, Ether 12:13). And finally, there is a brief reference to getting Shule out of Noah’s prison in Ether 7:18.
Summary: Maintain the use of prison without any determiner unless a specific prison is being referred to.