I will assume that the AI can't translate the knowledge it bases that prediction on into any form that is acceptable by human standards. For that makes the question self answering.
Such a simple and easy solution to implement if the setting allows it.
Once a month a secret crime is made under the watchful gaze of the government. You can sing several thousand people nation wide to stage crimes to be set. You can eliminate all forms of surveillance easily and can connect them using secret means like intelligence style messing and cells work.
Having the group stage the crimes to be able to fool humans perfectly. This is important as our laws only work on the human level not the gods level. That is if I saw me neighbor through his window shoot his wife and heard the gunshot and saw her body collapse to the floor. This could be a crime but also they could be practicing a play. Calling the cops at that point is 100% normal and to the human understanding the mere possibility of other things, magic or acting or whatever, is a point proven after investigation so it does not matter.
Human perception and understand is what laws are built on.
The best part?
It does not matter if the AI predicted the crime or not. Simply ask it
Simple. If it counted the crime then it has as much understanding as human observer which is enough to build a case on is our laws already.
But what if it did not count the crime? Then it much more smarter than humans and can even detect fake crimes.
Either way it is proven to be 100% functional and helpful.
Just as an extra point to address the issue of fake crimes.
It would be legally argued, and I am no lawyer, that the truth of the matter that those people did not commit a crime and that the AI can be fooled.
However a quick examination can be used to answer 1 question.
Did they people planned to seem like they did a crime beyond a reasonable doubt?
Because the systems, current ones, can't do anything beyond that.
Because that is all what the law requires. Not a single state on earth, or in history, can actually claim to do more or have done more.
Merely beyond a reasonable doubt. We hear all the time about a crime 20 years ago that is reopened and then the person thought to be guilty is then acquitted, whoops.
You can't then try to reject the system as even if you only prove that is like what we already have it has the added benefit of prevention the crime so it's like getting a 100% better computer with the same price. No reason to reject it.
While not mentioned in the question I think this fits in more than letting other crimes happen as the AI might be hardwired not never let that happen or anything similar, not to mention the moral problem.
However if the AI can predict sporting events down the smallest detail, rain fall, actors film choices, the stock market, the path random people take to work, what youtube channel will be popular this year...etc.
If it can do all this it would be very easy for a law change to happen as basically this proves that the AI can actually predict anything.
Intervene just before crimes happen. Proving state of mind, intent, preparation for the crime...etc to provide for a court as more concrete evidence.
Lets take Marcus for example. Marcus is a low life scumbag who is in and out of correctional facilities and always in trouble with the law.
One days he decides to rob a bank. Now he gathers the crew, buys the weapons and tools, stakes the places, plans on the time...etc.
Then just as his own car pulls in the bank he is meet with a SWAT team, or whatever you have equal to that, and then he is charged with the crime.
Now this is a much much simpler case to establish in a court of law and the tweaking of the current laws wont be as high as before.
In your earlier example of killing at birth no law or constitution in the world would allow that. The philosophy is complicated but basically it would be a crime even if backup with this AI.
However if you wait just before the crime is about to happen this narrows down the variables to the minimum and insures that you have sufficient proof, legal sense, to convict with the ultimate conclusion of the AI.
This I think is vital as it narrows it down, again it is important since the law deals with actual actions not magic predictions, and coupled with the 100% truth rate of the AI it should be enough to change the laws so that prevention of the crime before the crime carries the maximum penalty.
Let me give you another example. If the AI see Sara killing Matt in his apartment on Friday the 12th using her gun after she takes a long lunch break from work and eats a burrito on the way to his place while listening The Melvins.
This is more evidence than claiming that Sara will go to Matt to kill him on the 12th. Imagine that they have an affair and she goes to him for a quickie all the time.
The fact that she has gun does not equal intent to murder him, nor is she going there does as explained before.
So from a legal standpoint you want to limit the other factors and produce such a clear and obvious case. The needed proof from criminal cases is higher than civil cases and to trial Sara for murder without as much damning evidence as possible is very tricky from a legal since.
That is why if the AI can predict her course of action and words and all that it can be safely assumed that on this occasion indeed she will kill him.
This is flawed to an extent.
I can't deny it. The bank robbery for example is easy as it requires automatic rifles, just for example, and planning and other people...etc.
But say a guy gets drunks 2/7 days a week for years. Then one time he takes a knife and stabs his father. This is insanely complicated because he was doing just about everything the same exact way before but just this time decided to do the murder.
I'm sure that actual lawyers have more interesting thoughts on it.
Thought I'm not sure that the philosophy of the law is what you are looking for or not. Anyway hope it helps.