Probabilistic Dam Stab 2009
Probabilistic damage stability has recently been "upgraded" to what is called the 2009 regulation. The regulations can be found in MSC 216(82), Part B: Stability.
There are some handy explanatory notes which are known as MSC Circ. 1226, which describes regulations in a bit simpler way.
I have attached those, along with a paper that gives an introduction and summary to probabilistic damage stability.
Basically it is too complex for me to explain fully, but I think the regs. and the paper should give you a good start.
In general the calculation is a form of statistics, where the probability of the survivability of the ship in different damage conditions is calculated based on the regulations and given an index. That attained index must be greater than the required index (given by the length and type of vessel) in order for the vessel to "pass" damage stability.
Good luck with it! The statistics and regulations can be hard to grasp, and I don't think you can do the calculation without software. I recommend
NAPA, most of the major Class. societies use it as well.