In a time when there were no photographs the arresting soldiers needed to know which Jesus was. They would know who Judas was having seen him previously. Jesus had a huge public profile. Arresting the wrong person would have been a humiliation for Rome and would have shown that the self-proclaimed ‘perfect empire’ was not perfect at all. As a result the resistance would have taken full advantage of the faux-pas and Roman control of the population would be compromised.
Judas was a necessary tool used by the Romans and relatively cheap for them. Had Judas not participated Jesus would most likely not been arrested as the risk of mistake was too great.