How is a "conflict" between aircraft predicted and determined?
It is a bit of a grey area and the answers you'll get will depend also on which field of expertise you are in. I am involved in developing and standardising ATC surveillance systems, here's my take on it. 

Loss of separation is the simplest definition of the two and it has regulatory consequences. But even that one is not black and white. How do you determine the exact position of two aircraft? Suppose you have a 5 NM radar separation minimum and a radar that has an accuracy of 0.2 NM. If the two aircraft are flying parallel 5.1 NM apart at the same altitude there is a high probability that at some point the difference in radar measurements is less than 5 NM. Is that a loss of separation? To make it even more complex, radar tracking systems lag in turn detection; while an aircraft has started to turn 15 seconds ago, the tracking system may see that as radar measurement noise and may stubbornly paint a straight track depending on the tuning parameters. 

The definition of conflict you quote has little regulatory meaning but has its roots in workload estimation of aircraft traffic controllers. It is also used in conflict detection systems. Short term conflict detection systems predict the path of aircraft by extrapolating the current position into the future using speed and flight plan, usually augmented by the aircraft traffic controller with cleared altitude, speed, heading etc. If within a predefined time window (approx. two minutes) two aircraft are predicted to be below the separation minimum, an alert is raised. The exact method of prediction varies from system to system. Medium term conflict detection is similar, but depends more on the flight plan than on the current speed vector. The longer term the prediction, the higher probability of a missed conflict or a false alert

The big trick is to design a conflict detection system that has a low missed alert rate (otherwise it isn't effective) and a low false alert rate (otherwise it is a nuisance and will be ignored or turned off) at the same time. It is indeed a trade-off of probabilities.