Then the father realised that this was the exact time at which Jesus had said to him, “Your son will live.” So he and all his household believed.
“believed” is to put total trust in the Person of Jesus, in the sense of becoming a Christian. This is the first recorded instance of an entire family giving themselves over to Christ.
McGarvey shares that “We note here a growth in the faith of the nobleman. He first believed in the power of Jesus’ PRESENCE, then in the power of Jesus’ WORD, and finally he believed generally in Jesus, and his household shared his belief.” (TFG 159) and Matthew Henry observes that “Diligent comparing the works of Jesus with his word, will confirm our faith.” He also says that “…an experience of the power of one word of Christ, may settle the authority of Christ in the soul.”
The sickness of the child resulted in the salvation of the whole family. God takes that which is evil or bad in our lives and turns it around into great good. Can you trust Him to do this?