Preconditions for freeing a slave in Islam

I am told the precondition for freeing a slave is that he/she needs to be Muslim in first place, based on the hadith of Sahih Muslim, where a slave girl is asked "where Allah was" and subsequently the speaker argued that the prophet wanted to find out whether she was a Muslim or not. Incidentally there are other reports, which say a slave who delivered the child of master becomes freed upon death of master. Since these two dont reconcile, hence the question: what are the preconditions for freeing a slave in Islam? Search engines arent returning any answers.