John 4:53

‘So the father knew that it was at that hour in which Jesus said to him, “Your son lives”, and he himself believed, and all his house'.

There is a contrast here between differing forms of belief. Previously his faith had been that of those who saw signs and wonders, but gradually it had grown. Now it was a deep faith of commitment (expressed by the inceptive aorist of the verb) that responded to Jesus and His words. That was what was lacking in others.

‘He himself believed, and all his house.' That is, those who were of an age to believe. The whole household responded to what had happened on hearing the father's testimony. Like the Samaritans the family of the court official responded with full heart.

It is quite clear that this is a very different story from that of the centurion's son in Luke 7:2 and Matthew 8:5, the only thing in common being the healing at a distance which was something that Jesus must have done a number of times. These particular stories were recounted because they carried a specific message in a context. In the account of the centurion's son the centurion did not ask Him to his home, was confident that Jesus could heal at a distance without being told, and asked Him to speak only the healing word, whereas in this account the man's faith was not as great, although it was growing. For the centurion there was no rebuke, only praise, whereas for this official rebuke preceded action. The end result, however, was the same. They both finally come to a full faith.