Why certain "of" constructions do not need the definite article and some others do?

Question

Without federal inspection of meat, however, chances of contracting food-borne illnesses would be much higher and the everyday task of eating would be much riskier. (source: book We the People)

This sentence reads normal and commonplace, but when I try to discern what it is that distinguishes the three noun phrases in terms of article use, I couldn't quite identify it. I understand the reason behind the definite article in the last boldfaced noun phrase is that it is a specific reference while the other two generic, but what makes it so? What about the first two phrases that makes them non-specific?

Answer 1

Without the federal inspection of meat

This would work if a prior sentence had, for instance, discussed state and federal inspections and how they differ. Or if it had otherwise been put in the context of the overall process of inspection rather than a specific instance that has not yet been defined.

Note that there really should be some article given; if not the then a.

the chance of contracting

I would say this is really how it should be written.

Using the plural chances looks odd. The only way it would work is if it is talking about "chances" in the sense of buying ten lottery tickets and having ten chances of winning. But I'd say it's more natural to interpret the sentence as meaning the probability of contracting illnesses. And there is only one probability—so it takes the definite article.

In summary, I believe the sentence is better written as:

Without a federal inspection of meat, however, the chance of contracting food-borne illnesses would be much higher and the everyday task of eating would be much riskier.