A.T. Robertson Commentary John 4:53

"So the father knew that [it was] at that hour in which Jesus said unto him, Thy son liveth: and himself believed, and his whole house." — John 4:53 (ASV)

So the father knew (εγνω ουν ο πατηρ). Second aorist active indicative of γινωσκω. Inferential use of ουν.

Himself believed (επιστευσεν αυτος). Not just the word of Jesus (verse 50), but complete faith in Jesus himself as the Messiah, absolute use of πιστευω as in 1:7.

And his whole house (κα η οικια αυτου). All his family, the first example of a whole family believing in Jesus like the later case of Crispus (Acts 18:8).