“knew” (KJV)  is the Greek ginosko which menas to learn to know; to become acquainted with; to gain a knowledge of.  NIV translates as “learned.” Jesus came into the knowledge that the Pharisees had heard about His increasing popularity either through divine knowledge or, more likely, through having heard about it from natural sources.

McGarvey states:

“We have in these verses two reasons assigned for the withdrawal of Jesus into Galilee, namely:

1. The imprisonment of John the Baptist. Matt 4:12, Mark 1:14
2. Knowledge of the Pharisees that Jesus was baptizing more disciples than John. John 4:1

“The first gives us the reason why he went to Galilee; the second, the reason why he left Judea. Jesus did not go into Galilee through fear of Herod, for Herod was tetrarch of Galilee. The truth is, the absence of John called for the presence of Jesus. The northern part of Palestine was the most fruitful soil for the gospel. During the last six or eight months of John’s ministry we find him in this northern field, preparing it for Christ’s kingdom. While we cannot say definitely that John was in Galilee (Bethabara and Aenon being the only two geographical names given), yet he certainly drew his audiences largely from the towns and cities of Galilee. While John occupied the northern, Jesus worked in the southern district of Palestine; but when John was removed, then Jesus turned northward, that he might sow the seed of the kingdom in its most fruitful soil. But if there was a reason why he should GO to Galilee, there was an equal reason why he should DEPART from Judea. His popularity, manifesting itself in the number of his baptisms, was exciting that envy and opposition which caused the rulers of Judea eventually to take the life of Jesus.

“The Pharisees loved to make proselytes themselves. Matt 23:15 They no doubt envied John’s popularity, and much more, therefore, would they be disposed to envy Christ. The influence of the Pharisees was far greater in Judea than in Galilee, and the Sanhedrin would readily have arrested Jesus had he remained in Judea, John 7:1, 10:39 and arrest at this time would have marred the work of Jesus. Therefore, since it is neither sinful nor unbecoming to avoid persecution, Jesus retired to Galilee, when he remained until his second passover. By birth a prophet of Judea, he became, in public estimation, by this retirement, a prophet of Galilee. Though Jesus first taught in Judea, the ministry in Galilee so far eclipsed the work in Judea that it was spoken of as the place of beginning, Luke 23:5, Acts 10:37 and prophetically designated as the scene of the divine manifestation.” Matt 4:14-16 (McGarvey TFG 139-140)

In addition to the reasons given by McGarvey for Jesus to go to Galilee upon the arrest of John is the fact that John’s disciples would be scattered and Jesus would want to gather them in His arms as the Chief Shepherd.