There's welcome level headedness here. Who is most likely to carry out any wrongdoing? Someone who wants to, thinks they can get away with it, and has the chance.
It could be nicking someone else's biscuit, or abusing a child, or doing a bank robbery.
So who will molest your child? Someone you trust, someone who has plenty of opportunity, someone who won't be caught.
Nobody would actively choose a neighbour previously known to have committed crime. But 999 times in a thousand, nobody will know. And even less often, people will suspect that their charming neighbour murdered his last neighbour, defrauded a previous neighbour, or raped a previous neighbour.
The only offence you will get to know about is this one, and the purpose is to keep children more secure, for example the one with the child in the next door garden. She knows either to keep the child away, or to put a c.c.t.v. and/or a higher fence, and/or fence off an area of the garden closer to the house, or on the opposite side of the garden, as a children's area. (Maybe not have balls or frisbees or dogs in the garden at the same times as the child is unattended?)
It is extremely unlikely he will attempt contact with children in the area, because he knows he is under observation by local people, local police, and his wife. There may be ten potential other offenders living nearby, and nobody knows who.