I want to send an e-mail notification when probe A is down AND probe B is NOT down.
Is it right to use a Logic Probe of type 'not'?

Probe B checks an application server and 16 versions of probe A check services provided by the application server. If Probe B finds out that the application server is down, there is not need to bombard the application manager (which is me in this case ) with 17 e-mails.

You need to create to objects on map B, and A with same ip addres(to your probes work correctly, if your probe address dependent)
Then turn you map view mode to "Dependency" (top rigth corner of map), and add add dependecy
B->A - that mean A depend from B.
"B" must have only one service(to turn red on that service fail, if there is two services - it will turn yellow, and that wouldn't work)
"A" will have all your 16 services.

Thanks!