In Lancaster v Blackwell Colliery Co Ltd (1919), 89 LJKB 609 Lord Birkenhead LC said at p.611:
If the facts proved give rise to conflicting inferences of equal degrees of probability, so that the choice between them is a mere matter of conjecture, then, of course, the applicant fails to prove his case, because it is plain that the onus in these matters is upon him. But where the known facts are not equally consistent, but there is ground for comparing and balancing probabilities, as to their respective value, and a reasonable man might hold that the conclusion for which the applicant contends is the more probable, then the arbitrator is justified in drawing an inference in his favour.
Per Barry J in Horabin v British Overseas Airways Corporation  2 All ER 1016 at 453:
It very often happens that two different inferences may be drawn from one set of facts. For example, a motor car may cross a controlled crossing after the lights have gone yellow owing to wilful misconduct on the part of the motorist, but it may equally well have been due to a mere act of carelessness on his part in not keeping a proper look-out and not seeing the lights in time. If both those inferences are equally likely - if there is nothing to indicate that it was more likely that this was an act of wilful misconduct than that it was an act of negligence - then it is not established that wilful misconduct was the cause of the act. On the other hand, other facts may enable you to balance the probabilities as between those two possible inferences, and to say: Looking at the matter as a whole, and taking this point and that point into account, we as reasonable people think it more likely that the true explanation of this car going across the cross-roads when the lights were against it was, for example, that the driver was committing an act of mere negligence. If on your consideration of the whole of the evidence you are able to balance the probabilities in that way, you are entitled to say: On balance of probability, we think that a certain act was an act of wilful misconduct. In those circumstances in the present case if you think on balance that any one of these acts alleged against the servants of the defendants was an act of wilful misconduct, then, if that act caused the accident, the plaintiff will be entitled to recover the damages which he is seeking to recover.