To put the risk of duplication into perspective, ICAO has so far allocated around 10 million of the 16 million possible 24-bit addresses to individual states, for them to use on both civil and military aircraft.
That doesn't mean anything like 10 million Mode-S-equipped aircraft actually flying, of course - I doubt whether it's even 10 percent of that number in practice. For example the USA uses less than half of the one million or so addresses in its allocation at any given point in time.
One of the most common causes of duplicated 24-bit addresses is an undetected single-bit error (a 0 instead of a 1, or vice versa) which, if it occurs in the LSBs and in a country that allocates addresses sequentially (like the UK), is likely to match an address used on another aircraft.
The other main cause, in countries that reissue tail numbers (like the USA), is where an operator changes a tail number but fails to reconfigure the transponder to use the 24-bit address that matches the new registration. If the original tail number is then re-used on a different aircraft, both would end up using the same address.
Notwithstanding ICAO and EASA's exhortations, there doesn't seem to be any organised international effort to deal with the problem effectively. Unless anyone knows differently.