For bird Ingestion caused
Two probabilities at play here
1) the probability of what part of the engine will be damaged by birds
2) the probability of a stall for a given bird damage result.
In the large fan engines common to most large transports today (not turboprops) The highest probability for damage location is the fan. This is 10-100 times more likely than any other engine part.
A damaged fan alone may lead to an engine compressor stall, and if so, usually due to the resulting mismatch between the turbine workload between the Low speed and high speed turbines.
The Sully event was a rare outlier in a bird induced damage cause-effect