probability, odds, possibility, prospect, likelihood, opportunity, opening, occasion, accident, fortune, luck, fate, destiny, coincidence, speculation
Synonyms for Possibility are chance, probability, option,
Chance.
timechancefortuitycutstabsqueakwhackreliefchance
risk, chance, venture, lottery, speculation, uncertainty
unintentionally, incidentally, by accident, by chance, inadvertently, unwittingly, randomly, haphazardly
possibility, happening, chance, event, incident, accident, emergency, eventuality
gamble, chance, stake, venture, hazard, speculate, wagerchance, risk, play
occur, take place, come about, result, develop, transpire, come to pass, chance
fate, fortune, lot, portion, doom, nemesis, chance, karma, providence, predestination
If you are referring to luck as a concept without positive connotations, chance would be a synonym.
Some synonyms for the word discovered would include: detected, disclosed, brought to light, apparent, bare, ascertained, disinterred, come across, chance upon and bump into. This is only a few examples of the synonyms for the word discovered.
certainty (no doubt), probability or likelihood (greater than 50% chance), possibility (greater than 0% but less than 50% chance)