This answer suggests a standard of "beyond a shadow of a doubt". That type of term is very popular from an English Law perspective, which has varying standards of "proof". Among them:
- Probable cause (30-51% chance of the relevant fact)
- Preponderance of evidence (51%, or more likely than not)
- Clear and convincing (substantially more than 51% and a firm belief or conviction of the judge)
- Beyond a reasonable doubt (one would be willing to rely and act upon it without hesitation in the most important of one's own affairs).
Beyond a shadow of a doubt is, of course, even higher than this, although not used in English law (and some of a philosophical bent would question if it is ever achievable).
In a Jewish context, I think the last four (Preponderance, clear and convincing, beyond a reasonable doubt and shadow of a doubt) are a reasonable description of the perception of G-d in the four worlds, however this question is about Choshen Mishpat.
What are the relevant standards of proof in Judaism and when to they apply?
One famous distinction between capital cases and others is if it requires seeing vs knowing (עדי ראיה ולא עדי ידעה), but that is a standards of evidence issue, not a standard of proof.
What standard(s) of proof is/are required in Halacha with regards to Beis Din cases? My impression (which is vague) is that clear and convincing would be a pretty close approximation, but I'm not sure.