How do we say
The possibility of dying in a car crash here, is always at the maximum rate
correctly? Is that sentence correct? I don't want it to sound very formal.
This is just my two cents, but the phrase maximum rate denotes a sense of urgency that you may or may not want to replicate in a more mechanically sound manner. You might try some other words that carry urgency and the idea of "impossible odds." Stay away from the word rate as it's used more to describe a degree of progress, speed, or development (rate of change, rate of growth) and is not really suited to odds or probability. Here's something to go with the word possibility
You can use this example (or something similar) to sort of bring the threat of death forward from the realm of possibility, where now the driver (and reader) have to be afraid of it, evoking panic and intensity.
The only pitfall to the word possibility is that it's usually met with a sort of true-or-false reaction. Either something is possible or not. If you use words that describe odds, chances, or probability your fatal car crash goes from could happen to almost certainly will happen
Your other option is to approach from another angle like the other answers have:
These are just my suggestions, I hope it helped
If you don't want to sound too formal, I think these three are the best options:
To answer whether your original sentence is correct: You have to erase the comma, as it cannot be there. Apart from that, the sentence is too complicated and sounds awkward, but I wouldn't say it's ungrammatical, if you omit the comma, that is.