I have found a number of definitions but none are satisfyingly congruent with the usages that I have seen in legal contexts including several times on here, which generally use it to describe a quality of evidence, even the definitions which I have found through search engines in specifically legal dictionaries.
The definitions you found online and in legal dictionaries are likely correct. I suspect you found something such as:
The quality or condition of having strong moral principles; integrity, good character; honesty, decency. (Oxford English Dictionary)
This is the definition corresponding to the most typical (what many would call the "correct") use of the word. It is often used in phrases like "probity and fair dealing."
If you have seen other uses, in relation to the quality of evidence, this is an occasional misuse. See Footnote 54 in Matthew Gourlay, et al., Modern Criminal Evidence, Chapter 1:
There is an unfortunate trend in some recent judicial decisions of using the term "probity" as a synonym for probative value: see e.g. R v Durham Regional Crime Stoppers Inc, 2017 SCC 45,  2 SCR 157 at paras 43-47. "Probity" refers to moral uprightness and is not the noun form of the adjective "probative." If a new coinage is required, "probativity" would be preferable.