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. 

Jesus speaks of the Holy Spirit Parakletos, which was an advocate who spoke on behalf of the defendent, but note that that this defence counsel can turn prosecutor:

And when he comes, he will convict the world concerning sin and righteousness and judgement… (John 16:8)

Here then, to convict is to provide the compelling evidence that is laid before everyone.

In this the follow up post on Christian faith, we now understand that the second part of the two-fold definition concerns what is ‘not seen’.  The apostle Paul helps with understanding of what is ‘unseen’:

… we look not to the things that are seen but to the things that are unseen. For the things that are seen are transient, but the things that are unseen are eternal.  (2 Corinthians 4:18)

And what is eternal? Why, God of course!

No one has ever seen God; the only God, who is at the Father’s side, he has made him known.  (John 1:18)

The second person of the trinity, Jesus the Son, is seen, but his Heavenly Father has never been, for he is in heaven, as the Lord’s Prayer says.  

In Romans, Paul asserts that faith is the prerequisite for any to be credited righteousness and is the only requirement, not any personal work

That is why it depends on faith, in order that the promise may rest on grace… (Romans 4:16)

And that includes the work of certitude.  To say of oneself ‘I am certain I am right with God’ might stand if that conviction is based on the compelling evidence resulting from a walk of continual repentance; but such self-declarations come unstuck if that certainty is confused with the factual.

Personal salvation, the product of being made right with God, can only be known after the fact, not before it.   A strongly held conviction then remains a belief or faith: God requires enacted faith, or ‘trust’ from his elect.  In this regard, faith and risk are synonymous.  And Paul offers reassurance that taking a risk on God will not backfire.  God and His promise of salvation is a ‘hope does not put us to shame’, Romans 5:5.