The effect is to emphasize the fulfilment of Jesus’ words to Peter (13:36), and to make it clear that ‘Peter cannot follow Jesus, until Jesus has died for him’ (Fenton, p. 182). Both for John’s readers, and for the early church generally, this is not Peter’s final scene. As serious as was his disowning of the Master, so greatly also must we esteem the grace that forgave him and restored him to fellowship and service. And that means–both in John’s Gospel and in our lives–that there is hope for the rest of us.

The Gospel according to John (The Pillar New Testament Commentary (PNTC)) . Eerdmans Publishing Co – A. Kindle Edition. 

Simon, Simon, behold, Satan demanded to have you, that he might sift you like wheat,  but I have prayed for you that your faith may not fail. And when you have turned again, strengthen your brothers.”  Peter said to him, “Lord, I am ready to go with you both to prison and to death.” Jesus said, “I tell you, Peter, the rooster will not crow this day, until you deny three times that you know me.” Luke 22