Notwithstanding the point I made a few posts back (that with cctv and forensics it is possible to prove beyond any doubt the guilt of someone?)
Actually, neither CCTV nor forensic (nor the combination thereof) can guarantee someone's guilt. Video images can never provide a 100% positive identification, and you're hugely overestimating modern forensic science if you're under the impression it could establish guilt beyond any and all doubt.
Trouble with the custodial option, though, is that a convicted offender could escape and kill, or rape a child, again.
Sure, they MIGHT escape... though if you maintain and run your prisoners properly that's a very minor concern.
And sure, after they hypothetically escape they MIGHT commit their crimes again... or they might not.
However, what MIGHT happen is not a valid reason for killing them.
This makes me wonder: if it were possible to foresee it, would someone who's against capital punishment in all circumstances now change their mind knowing that this notional escapee is fated to commit an identical crime against a member of their own family?
It is not, however, possible to foresee it. Besides, there's a huge glaring flaw in your scenario: if it's possible to foresee that someone will escape and kill a member of a specific family (or indeed, kill anyone at all)... you can just prevent their escape to begin with. You don't need to kill them for that. Unless you seriously expect prisons to be so utterly and completely incompetent that we might as well get rid of them entirely.
"Uh oh, the prisoner has escaped."
"The one we foresaw would do exactly that followed by murdering some very specific individual?"
"That's the one."
"Didn't we foresee how he would escape!?"
"You'd think so, given this foresight was apparently accurate enough to specify exactly who he's going to kill even though they've never met or have any link whatsoever. But no, the vision/foresight/whatever was remarkably vague on that point."
"If only we just paid special attention to this prisoner and increase security!"
"Well, that would've been pointless, obviously, since it was already foreseen."
"Oh that makes... wait, what about that guy on some internet forum who kept saying this particular foresight meant we ought to kill the prisoner to prevent the foresight/vision from coming true?"
"Yeah, we should've listened to him."
"No, no... if preventing the prisoner's escape by taking sensible security measures was impossible because he was fated to escape... would it not be impossible to kill him anyway since that would be messing with fate?"
"...dude, I'm a prison guard, not a philosopher."
"Well, are we at least going to warn the person he's fated to kill? Maybe move them out of the country?"
"What? No, it's too late now."
"But there's got to be at least a 1000 miles between them still!"
"Dude, it's fated."