Jeremiah 31

But this is the covenant that I will make with the house of Israel after those days, says the Lord: I will put My law in their minds, and write it on their hearts; and I will be their God, and they shall be My people.  No more shall every man teach his neighbor, and every man his brother, saying, ‘Know the Lord,’ for they all shall know Me, from the least of them to the greatest of them, says the Lord. For I will forgive their iniquity, and their sin I will remember no more.” vv.33-34

Read chapter 31
We read often in the New Testament about the new covenant, but what exactly is the new covenant?  Well first off to have a new one you have to have an old one.  And who was it that had the old covenant?  Israel.  Israel had the old covenant which was the law of Moses.  So this new covenant is a new law that God is making with His people Israel as we read in verse 31 of this chapter, "Behold, the days are coming, says the Lord, when I will make a new covenant with the house of Israel and with the house of Judah ."  This new covenant was not going to need people to teach the law for it will be written on their hearts.  They'll be no door-to-door evangelism.  
If someone were to do something against this law, their hearts would condemn and correct them, not needing to go to a judge or court or anything.  This obviously is not something we see now in our world, but will be the law in the kingdom of God.  It will no longer be a question or even a thought if there is a god, for from the least to the greatest all will know Jehovah God.   In this time the Lord will forgive their sins and remember them no more.  He's not just sweeping their sins under the rug so to say, but has already judged them and moved on.  For God to remember no more means that He will not go back to change His mind on a matter, once He has known and decided a matter it is done.  Kind of like double jeopardy of not being allowed to be tried twice for a crime.
We may not be Israel, but no doubt this law of the new covenant will be spread throughout the whole earth to every person living in the kingdom.  We'll no longer have need for policemen, how about that.  But in till then let us live "teaching his weight and every man his brother saying 'know the Lord.'"