In a hostile environment, it is important for a transmitter to make its wireless transmission invisible to adversaries because an adversary can detect the transmitter if the received power at its antennas is strong enough. This paper defines a detection probability model to compute the level of a transmitter being detected by a detection system at arbitrary location around the transmitter. Our study proves that the probability of detecting a directional antenna is much lower than that of detecting an omnidirectional antenna if both the directional and omnidirectional antennas provide the same Effective Isotropic Radiated Power (EIRP) in the direction of the receiver. We propose a Minimizing Detection Probability (MinDP) routing algorithm to find a secure routing path in ad hoc networks where nodes employ directional antennas to transmit data to decrease the probability of being detected by adversaries. Our study shows that the MinDP routing algorithm can reduce the total detection probability of deliveries from the source to the destination by over 74%.