Overview
Rather than using point values to represent random quantities, as in deterministic approaches, probabilistic approaches to risk assessment assume a distribution for each random quantity. Results are presented as probability distributions, or the bounds of probability distributions.
The probabilistic approach to risk analysis estimates risk as a function of:
 the severity — or magnitude — of each consequence
 the likelihood (probability) of the occurrence of each consequence
In the safety domain, the consequences and types of events assessed are generally adverse (they represent losses, that we try to avoid). In other areas such as finance, events and their consequences may be either positive (profits) or negative (losses).
Consequences are expressed quantatively (for instance, the number of people potentially injured) and their likelihoods of occurrence are expressed as probabilities.
Course material
Other resources
We recommend the following sources of further information on this topic:

Course material for the TU Denmark course on Risk and Safety in Engineering, by Prof. M. Faber

Slides which supplement the book Risk Assessment — Theory, Methods and Applications

Slides on Fault Tree Analysis which accompany the book System Reliability Theory

Problem sheet for the book Reliability of safetycritical systems

The ReliaWiki, a wiki on reliability engineering

Briefing notes on control of risk in health and safety, by the Institution of Engineering and Technology (IET)