Is it obligatory to inform the husband about an adulterous relationship that was discovered by chance?

Your duty is to advise the man and the woman and urge them to repent if you are certain of the matter. If they repent, then conceal their sin. If they do not repent and you find no way to stop them except by informing the woman's husband, then inform him. It is important to note that accusing people of indecency without clear proof and spying on them are among the major sins.