‘And they seized him, and led him away, and brought him into the high priest's house. But Peter followed afar off.'
So Jesus was arrested on the Mount of Olives and led away, and was brought to the house of the High Priest. The disciples meanwhile had scattered. Jesus had forbidden resistance and they wanted to avoid arrest. But Peter, determined not to let Jesus down, and so that he could prove his loyalty, did not go far, and when the arresting party moved off, he followed them at a distance (accompanied, we learn in John 18:15, by another disciple, which was probably John himself).
‘Peter followed afar off.' It would not have been wise to do anything else, but Luke's words may well be intended to include the thought that Peter's heart was not as it should have been. They are a warning to his readers lest they too ‘follow afar off'.