A judge finds a person guilty based on credible witnesses to the violation.
To be more precise, the Bible's standard is two or three witnesses.
God is triune, and is Himself three witnesses.
Jesus could not convict an adulterous woman because the witnesses went away and did not testify.
Correct. The law stated "two or three witnesses establishes a matter. On the testimony of only one, no one can be condemned."
Yet, since God is triune, and bears witness to the fact that man has (generally speaking) rejected Him, therefore they are condemned to separation from Him, unless they turn back to Him, and that if they confess with their mouth the Lord Jesus and believe in their heart that God has raised Him from the dead, they will be saved. (Romans 10:9)
Until that point, they are condemned.