In Czech language, the word "вероятность" sounds like "pravděpodobnost" [правдеподобность], and means "it is truthlike" (подобно правде). This made me look to Russian word - вероятность. Does it have something to do with "вера"? For example "ятный вере" or something like this, where the first word is obviously an archaism...
My two cents. It is obviously connected to
вера it's just that this connection is not that straightforward as it claimed to be in other answers provided: it is neither direct derivation or a straightforward calque.
It is actually another cognate word,
вероятие (вѣроятie in old orphograhy) from which the word
вероятность had evolved. Вероятие can be translated as
likelihood, so it is synonymous to modern Russian достоверность, возможность (besides the fact that it had been used as in sense of
вера as well).
To my knowledge
вероятие is not very old word, most probably it came to usage in XVIII century. For example in book "Приключения Фемистокла" by Fyodor Emin (published in 1763) we can find following quote:
Многия так от докторов как и от безумных баб облехчение получают; что дѣлается чрез сильное воображение желаемаго, и вѣроятие тому, кто нас лѣчит.
This word has not been some kind of bookish slang not quite used in colloquial speech. On the contrary it was quite colloquial and less pathetic than
Moreover, it even had been used in so-called
феня jargon (some stick to term cant language), the slang of russian semi-crime vagabonds:
дать вероятие meant to check out, to test something/someone.
вероятность has been in use at least from late XVIII century and it's first usages had not been related to any strict scientific terminology. Is had been used by analogy with вероятие and gradually (and relatively slowly, word вероятие had been use in XIX century as well) replaced first form.
One of the first usages can be find in Eulers Russian letters dated 90-s of XVIII century:
Вѣроятность того мнѣния, что каждая неподвижная звѣзда есть такоеж Солнце как наше.
Just to avoid possible questions: Euler lived in Russia for years, had been a fluent speaker and had no problems with writing in Russian.
Wiktionary article on вероятность cites Vasmer's Etymological Dictionary:
Происходит от прилагательного вероятный, далее от др.-русск., ст.-слав. вѣрѫ ѩти, букв. «принять веру», «уверовать»
- вероятный - такой, в который можно поверить;
- вероятность - мера веры во что бы то ни было
So, at least Vasmer agrees with you on connection between