Paul the apostle was an interesting man. His early life was devoted to the study of the old testament. At some level, he wanted to please God. Caught up in the religious spirit of the jews, he hotly pursued Christians. He had been given authority to jail them as heretics.
Jesus decided Paul's time had come and blinded him, knocking him off his donkey. I'm sure once Paul realized who was talking to him the fear began. Here he had been imprisoning and killing Christians for believing Jesus was the messiah.
Later in his life he was shipwrecked on an island where something happened that was the perfect example of the way we should react to threatening situations. He was adding a bundle of wood to a fire when a snake came out of the bundle and bit into his arm and hung on. What did Paul do? Did he panic and run in circles screaming that he had just been bitten by a poisonous snake? No. He shook it off into the fire and went about his business.
I'm sure the bite hurt, but he knew the Living God and trusted Him in a situation that would normally spell big trouble. Many fearful people would be saying, "great, not only am I shipwrecked, now I've been bitten by a snake!"