Now faith is the assurance of things hoped for, the conviction of things not seen.  (Hebrews 11:1)

A conviction is a firmly and strongly held belief and in the ESV Bible translation it stands for the Greek word ἔλεγχος elegchos, which can mean ‘test’ or ‘proof’, but here it means to believe fervently.

A court conviction is the decision based on solid and compelling evidence, and it is the verdict based on the balance of that evidence.