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There's no visible metric for the chance of zombies having a weapon stuck on them afaik. But based on my own eyeballing with standard apocalypse population, I'd wager the rate is somewhere between 10%-20%. And that is shared between an axe and other, more mundane things like a scissor or letter opener.
Based on my longest save file, I'd say you'll come across somewhere around 10 hand axes after a year of zombie slaying. The other types of axes may have a chance to spawn, but hand axe is the most common among the axe category.