Asking a feverish patient if they believe in the power of Christ unto salvation is not standard modern medical procedure. Nevertheless, Zeezrom was certain that this was a physical manifestation of a spiritual illness, and so the question is appropriate. It was a signal of his repentance from the former teachings of the Order of the Nehors and his willingness to accept the Nephite religion as Alma and Amulek had explained it.
When Zeezrom confesses faith in the redemption of Christ, Alma asks God to heal Zeezrom. It was done. The end of this episode sees Zeezrom not only healed, but also converted, from defending the Order of the Nehors, into a preacher of the Nephite religion.