Suspicion will raise as you kill your victims, in order to keep it low, you should not kill any victims outdoor.
As the suspicion levels rise, heroes will come to your mansion to attack and kill your minions.
The higher levels of suspiction should attract even more heroes to your mansion, so if you can't face them, keep the suspiction as low as possible.
Suspiction level will lower overtime, also events will be triggered through the gameplay, such as hacking and killing all witness for a small amount of gold