To "engage" is to become consumed in, or absorbed in, in terms of an activity. For example, to be engaged in reading. This means that your total focus is on reading.
Now to be engaged by, that is the reverse meaning (passive meaning, as in, you are not doing it; contrarily, it is being done to you).
For the meaning of "be engaged by," that means for the police and military to go into an offensive stance and be consumed in the activity of fighting or war. In simpler terms: they will attack whomever they are engaging.