The short--and probably annoying--answer is that it is entirely up to you. This is something that has little to no bearing on actual game play, except insofar as it impacts setting design, and thus your own (as DM) handling of game play. For instance, if you decide on a high ratio of adventurers (say, 1% of population), then PCs are more likely to encounter other groups, especially in dungeons. But if you take a more rare proportion (say 1 in 10,000 or fewer), then your PCs would rarely if ever encounter other adventurers.
Some other factors to consider....
Region: there might be fewer adventurers per capita in a heavily populated region than wilderness. You might have frontier towns where every third person is an adventurer and the majority of the economy is about supporting the adventuring life (sort of like a tourist town), vs a more heavily populated region that is comparatively tame. This also depends upon assumptions about your own setting: is it more "Points of Light" ala 4th edition or set in Italy during the height of Rome? Or maybe Colonial America is a good way to think about it: you had the more populated and "civilized" Atlantic colonies, then the frontier regions. There are adventurers in both areas, but a higher proportion in the frontier: people seeking their fortune, looking for gold and glory, etc.
Another factor is what you consider an "adventurer" might change in different areas. In an urban setting, an "adventurer" might be a street urchin, whereas in an agrarian setting farmers might become adventurers as they defend their home from an orc invasion. Depends on the campaign.
Sometimes "adventurer" is defined as a leveled person: someone who has levels in a character class. If that is the case, then it is probably a higher percentage than people who actively go on "adventures."
I would also imagine that more people try it out quickly retire when they realize what it entails. Sort of like high school graduates who go on a road trip in the summer after they graduate, but then go back to school in the fall.
A related topic is how many adventures are in different tier ranges? Let's say the ratio is 1 in 1,000 are adventurers. So in the Waterdeep region that would be 2,000 adventurers (that makes more sense to me than 1 in 10,000, which would only be 200...maybe 1-2,000 makes sense). I would imagine that the majority of those 2,000 are low level, say 1-4th level. 75% (1500)? Most either don't continue or die off before they reach 5th level. Then at 5-10th level, maybe you have another 15-20% (300-400), maybe 5% (100) are 11th to 15th, and just a handful, maybe 2% or less (<40) are 16th+.
One more thing by way of conclusion. I would consider this a related question to the degree and amount of magic in your setting. While the D&D default is pretty high magic, it can be run low - or at least with very few spellcasters and/or magic items. Similarly with adventurers and to what degree it is part of daily life.
