The fourth minimal fact about the resurrection of Jesus Christ presented by Dr. Gary Habermas and Dr. Michael Licona in their book entitled The Case for the Resurrection of Jesus is that James, the skeptical brother of Jesus, was radically converted.
Both Mark and John report that Jesus’ brothers were not believers during His ministry. James earthly brotherhood to Jesus is attested by Paul in 1 Corinthians as well as non-Christian historian Josephus which provides multiple attestation for his initial disbelief.
Again, it is important to recognize that this does not rely at all on the divine inspiration of the Bible. I do believe the Bible is divinely inspired, but I recognize that you may not. However, I think that we both can agree that, when doing history, we can generally rely on the accounts left behind by historians. Even if you will not grant the Bible infallibility, the inclusion of this potentially embarrassing fact would seem to be authentic.
It is important for influential teachers to have followers, and if half of the biographers of Jesus Christ reported that even His own brothers did not believe Him, that would not say a lot for His message. This doesn’t seem to be any type of exaggeration or beautification of the story of Jesus. If anything, it seems to be potentially embarrassing. It doesn’t seem like Mark or John would have a reason to report that James was skeptical unless he really was and they were trying to do accurate history.
James is then recognized as a leader in the church in Jerusalem in both Acts and Galatians, and his ultimate martyrdom is attested to by Josephus, Hegesippus, and Clement of Alexandria. He was martyred for a reason, and that reason was his Christian faith.
What caused such a drastic conversion?
Like the disciples and the apostle Paul, he believed that he had a personal encounter with Jesus Christ.
“Although the personal appearance of Jesus to his brother James is reported only once in the New Testament (1 Cor. 15:7), it has the force of being part of the church's earliest tradition, as reported by Paul. Further, critical scholar Reginald Fuller explains that this is sufficient. Even without it, ‘we should have to invent’ such an appearance in order to account for two things: James's conversion from skepticism and his elevation to the pastorate of the church in Jerusalem, the center of ancient Christianity.”
Even if you do not believe there is sufficient evidence to believe that James claimed to have seen the resurrected Savior, there is undoubtedly something that happened to him. He was skeptical of his own brother’s claims, and he ultimately went to the grave because of his belief in his brother as the Lord and Savior of the world. Something must have happened; there must have been some event that motivated him to alter his perspective.
Again, affirming that James believed he saw the resurrected Jesus does not mean that Jesus literally rose, but this is another piece of evidence that needs to fit into the puzzle. So far, we know that Jesus actually died. We also know that the disciples, Paul and James all claimed to witness the resurrected Jesus at different times yet were all dramatically changed by these experiences. They were willing to die based on what they had witnessed firsthand. If they knew they were making the whole story up, it seems unreasonable to believe that they would go to the grave over a lie. It seems much more reasonable to conclude that they genuinely believed they witnessed Jesus Christ and were willing to die for that belief.
 Gary R. Habermas and Michael R. Licona, The Case for the Resurrection of Jesus (Grand Rapids: Kregel, 2004), Kindle Locations 611-614, Kindle Edition.