Not being guilty of killing a son of G-d?!
Not
everyone is a barbarian, you know.
Sitz im leben, old chum. You can't judge the past by contemporary standards.
What you or I might think barbaric is standard practice then. I mean, we consider things barbaric that were commonplace fifty or a hundred years ago, let alone, 2,000. I mean flogging, crucifixion, etc ...
D'you mean in response to his own conscience? From what evidence we have, that's highly unlikely. Pilate was eventually recalled (36AD) for brutal and heavy-handed dealings with those beneath him. His track record hardly speaks of a man of conscience, and what's just one more troublesome Jew in the scheme of things.
Pilate's problem is Caiaphas wants Jesus dead, but won't do it himself – Caiaphas could have Jesus stoned for blasphemy. Something is off and Pilate wants nothing to do with it. Caiaphas threatens to complain to Rome if he does not take robust action, but Pilate suspects this is because Caiaphas can then point the finger at Rome. If Pilate does as Caiaphas wants, he makes a martyr of the man who seems to have considerable support, especially in the countryside.
So he manages to turn the tables – if Christ is to die, it's because the Jews want him dead, not Rome. His performance before the crowd satisfies the Sanhedrin and the people, puts the blame on their shoulders, and lets him and Rome off the hook – all in all, quite deft footwork on his part.
Pilate is not stupid –
Here's Jesus, a man who clearly can't, or won't, keep quiet, and seems to have walked quite knowingly into the trap his enemies have set for him. He makes no attempt to save himself (Jesus could have shown to trial for the charade it was). He seems bent on His own destruction.
So Pilate bargains his life and career on the silence of a man who seems to have a death-wish and will not keep quiet? He'd be mad to do so.