Intuitively, P(A|B)>P(A|Bc),
since Peter will be in a rush to install his alarm if he knows that his
house will be burglarized before the end of next year.
(b)
Intuitively P(B|Ac)>P(B|A),
since Peter is more likely to be robbed if he doesn’t have an alarm by
the end of the year.
An explanation might be that in part a,
we assume Peter to be driven to not let burglars rob him, but in part
b
we assume the burglars to not necessarily be as driven, since we assume
that if the burglers know that Peter will install an alaram before the
end of the next year they might not rob him. If the burglers are driven,
they might actually be more inclined to rob Peter sooner, before he
actually installs the alarm.