Owen,
Chances may be very slim but does happen. Big sky theory works until an aircraft comes the other way with TCAS not working. Just take Uberlingen, a lot of little things add up to one big one.
You can say as many times as you like "it can never happen here", but thats just a self-assuring placitude. The day you start believing that is the day it can happen.
Im praying it doesnt, but even I can say it could happen to me. I've only had one breakdown of separation and I still kick myself for not seeing it sooner. (radar separation dropped to 4.5nm instead of required 5). Believe it or not a Jetsream41 overtook (or tried before I gave avoiding action) an A320. Once again there was multiple factors, I couldnt get lower for the Airbus so it had to level off relatively high and quite close to the aerodrome, The jetstream was on descent through the level, RT was really busy (Airbus couldnt get her call in), AIrbus threw everything out to slow down (every controller who saw the reply was amazed at how quickly the speed scrubbed off the jet), I didnt see the closing speed, I didnt stop the Jetstream off sooner. It was my fault nobody elses, before airbus operator thinks I am blaming them, but just shows more than one factor has a play in any circumstance.