Etymology of "probably" by etymonline

late 14c., "likely, reasonable, plausible, having more evidence for than against," from Old French probable "provable, demonstrable" (14c.), from Latin probabilis "worthy of approval, pleasing, agreeable, acceptable; provable, that may be assumed to be believed, credible," from probare "to try, to test" (see prove). As a legal term, probable cause "reasonable cause or grounds" is attested from 1670s.

Probable cause (used with reference to criminal prosecutions), such a state of facts and circumstances as would lead a man of ordinary caution and prudence, acting conscientiously, impartially, reasonably, and without prejudice, upon the facts within his knowledge, to believe that the person accused is guilty. [Century Dictionary]

Related: Probableness.