In "Doctrinal Discussion" Jason Lindahl writes:

What was the determining factor in Saul's conversion? To the end of his days, this unlikely apostle testified that it was the fact that “last of all [Jesus] was seen of me also” (1 Cor. 15:8). The Galilean Carpenter, who had most certainly been executed on a Roman cross and buried and sealed in a tomb, appeared to Saul alive and well. In other words, Saul was convinced by the resurrection. Perhaps he did not immediately think of it in that way; he only knew that the encounter with Jesus had supernaturally changed him. But later, he added Jesus' appearance to him to the long list of Jesus' other post-resurrection appearances as proof of the resurrection (1 Cor. 15).

Source: Building Christian Relationships: Adult Teacher's Insights, page 43.