"I don't believe in chance."
Translation:Já v náhodu nevěřím.
Why in this case is the word V followed by accusative case? should it be: Ja v nahode neverim?
No, it shouldn't. "V + locative" talks about something beeing located somewhere and that isn't the case.
You can probably think of it as a phrasal verb: "Věřit v + accusative (Boha/náhodu) = Belive in (God/chance)"