Might have been killed or could have been killed.

wangqh2696122But for the arrival of the police, you might/could have been killed.

The red part is not making any sense. To use the correct context, we need to change it: If not for the police arrving in time, you might / could have been killed already.

I read it as "Had it not been for the arrival of the police, you might/could have been killed."

I'd choose "might," because the expression "but for the arrival if the police" is rather high register, and "You could have been killed" is a bit lower register.

Both "might" and "could" are correct, natural and common.

By the way, what do high register and low register mean?

By the way, do you see any difference between "could" and "might" here?

It's a sort of standard by which certain usages are measured or compared.
At the bottom would be slang, followed by casual conversation.
Educated professional people sometimes maintain a higher standard of language.
There's formal language, such as you would use in a term paper.
They often say that the higher registers would be suitable for an audience with the Queen.

wangqh2696122By the way, do you see any difference between "could" and "might" here?

Answered.

wangqh2696122By the way, what do high register and low register mean?

See
See

CJ

dimsumexpressThe red part is not making any sense.

It is correct and natural; see Avangi's first post.