The growing density of drone traffic due to the increasing popularity of drones will cause frequently occurring traffic conflicts. This creates the need for reliable traffic conflict detection methods to minimize the number of mid-air collisions. A method to cooperatively detect traffic conflicts is the periodic exchange of beacon messages among neighboring drones. By receiving beacon messages containing status information, each drone becomes aware of arising traffic conflicts. Hence, conflict detection reliability inherently depends on successfully receiving beacon messages. However, a mapping from the beacon message reception probability to the conflict detection reliability does not exist yet. Therefore, we present at first a mathematical model which allows us to compute the beacon message reception probability in drone ad-hoc networks which use the slotted Aloha medium access control protocol. Subsequently, we introduce two novel metrics namely conflict detection probability and detection distance. These novel metrics are required since existing metrics have been found unsuitable for the analysis of the conflict detection reliability. The novel metrics allow statements about the reliability by taking the probability of receiving beacon messages from conflicting drones as well as the conflict scenario into account. Our results show that the conflict detection reliability strongly depends on the choice of physical and medium access control parameters, especially the number of information bits per complex symbol and the number of beacon message broadcasts per second. Moreover, we show the existence of an optimum choice of these parameters which maximize the conflict detection reliability in a specific scenario