Collocations for probability - noun

high, real, strong
There is a high probability that it will snow tonight.

greater, increased
low
equal
All callers had an equal probability of being chosen.

relative

degree
We can say with a high degree of probability that the poem was written by Shakespeare.

have
increase
decrease, reduce
assess, calculate
predict
estimate
determine
affect, influence
genetic factors that influence the probability of becoming sick

probability for
measures to increase the probability for a sustained recovery

probability of
This surgical procedure has a high probability of success.

in all probability
In all probability she wouldn't come even if we invited her.

on a/the balance of probabilities (BrE)
On the balance of probabilities, the pilot suffered a stroke before the crash.