Of course, since P(Child Attacked) is so very low it's still not a huge deal.
It's not really backwards. That sort of inversion is exactly part of Bayes' Theorem.
Picking numbers from thin air:
Let's say are related to 30 people know 200 and you encounter 10,000 random strangers and you have a 1 in 100 chance of an attack. Well the odds a specific random stranger attacks your child given the above assumptions is less than 1/2,000,000. The odds a specific person they know attacks your child would be less than 1/20,000 and the odds that a given relative attacks your child would be more than 1/6,000. Now who would you focus on? (What about a predator that has a 50% chance of attacking someone well he is still under 1/6000 because there are so many other people for them to attack.)
PS: Given my child's particular environment you should focus on relatives and people you know.
I'm sure that's true, but it doesn't answer the real question. For most parents, the question is: given my child's particular environment, what is the greatest threat to him?
Doctorow is saying: given that your child was attacked (and no additional information), the attacker is more likely than not to be a relative. That seems backwards.