When you have to make a witness statement for court
supporting evidence for serious allegations: This is an extension of what is said above, or a special case.
Courts will assess the inherent probability or improbability of an event. It of itself is a matter to be taken into account when weighing the likelihood of what you say against the other evidence available.
This does not mean that serious allegations require a higher standard of proof.
Basically, the more improbable the event, the stronger must be the evidence to prove it.
Much depends on the context within which the events are said to have happened.
In the case of In Re Dellow’s Will Trusts [1964] 1 WLR 451 it was said, "The more serious the allegation the more cogent is the evidence required to overcome the unlikelihood of what is alleged and thus to prove it".