In the UK the Health and Safety Executive takes the lead on the way this is interpreted, at least in the context of workplace safety under the Health and Safety at Work Act. The way they take decisions is described in Reducing Risks Protecting People. This shows that the level of precaution is very high. You can also explore other aspects of the HSE's approach to risk from their risk management homepage and expert guidance.
The simplest approach to precaution is to ensure that any options you are deciding between are 'safe', in that, for example, they satisfy HSE's requirements as outlined in the links above. It is generally too complicated to attempt integrated risk management by considering, and valuing, safety risk alongside other risks within a single management system.
In practice safety risk analyses have to aim to be more comprehensive than business risk analysis: it is longer before the law of diminishing returns sets in. Safety risks are generally measured in terms of frequency as the measure of likelihood rather than probability. This sometimes causes confusion, though it should not. Consequently results are sometimes presented as fN curves rather than S-curves. fN curves chart the frequency which which events in which N or more people are killed occur. (S-curves chart the probability of not exceeding a specific severity of consequence.)
Safety risk modelling often uses tree-like structures to enumerate the many ways that the future might unfold. Event trees start from a certain event and identify the ways in which it can develop. Fault trees identify the different ways in which a specific event might have arisen.