It is cumulative.

https://ionactive.co.uk/resource-hub/glossary/accumulated-dose

Radiation is not a matter of chance, but a matter of how much.

Every day, your body will probably generate at least one cell that would be cancerous if it wasn't for your immune system. If that probability goes up slightly as a result of mildly increased radiation that day, it likely won't overload the immune system's capacity to deal with it. If it is overexposed to radiation, eventually the greater probability of cancerous mutations exceeds the immune system's capacity.

It's probabilistic when it's 1 particle at a time.

At these rates of exposure from radiation it becomes primarily cumulative because at some point it's not a question of if you'll damage some cells or not, it's a question of if you're damaging them faster than they can repair or not.

There's still a probabilistic factor in when it leads to medically relevant damage and of what type, but it follows a pretty predictable scale dependent on prior dose