How probable is it that someone can get a liver transplant in 9 months?

Depends on how ill: Liver transplants come from live donors or deceased donors. Deceased donor organs are "allocated" by the candidate's meld score which indicates how ill they are. The higher the score, the more likely to get an organ, but also the more likely the patient is to die without a liver. With the organ shortage, death is a real possibility. So, the 9 month cut-off is not the most helpful way to think.