Three aircraft were scheduled to depart Melbourne via the 150 radial. VH-KDK and VH-WZI were vectored left of track to allow the faster aircraft, VH-EWL, to safely overtake both of them. A small closing speed existed between VH-KDK and VH-WZI but normal climb performance was such that vertical separation could be expected before radar separation approached minima. The Departures controller in training decided to place VH-KDK back on pilot navigation by instructing the pilot to track direct to Cowes. This resulted in VH-KDK and VH-EWL now being on gradual converging tracks. The trainee thought that VH-EWL would have drawn in front before both aircraft were back on track. In this configuration the aircraft were handed off to the receiving Inner Sector radar controller who was made aware of the converging aircraft and the possible need to alter one of the aircrafts tracks at a later stage. The Inner Sector controller knew that while the separation minima inside 30 miles was three miles, this increased to 5 miles further out. His judgement was that immediate action was not required but that separation needed to be monitored. The Inner Sector controller became distracted when VH-WZI had not made a radio call when transferred from Departures as well as being distracted by other traffic in the Ballarat/Yarrowee area. When he returned his attention to the convergence of VH-KDK and VH-EWL these aircraft were beyond 30 miles from Melbourne but with only three miles lateral separation. A turn was initiated and the required five miles separation was established. Significant Factors The following factors were considered relevant ot the development of the incident: 1. The Inner Sector radar controller was distracted by other aircraft. 2. The Inner Sector radar controllers scanning of the traffic under his control was inadequate. 3. The Inner Sector radar controller did not ensure that the aircraft remained adequately separated.