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