use of definite article 'the' with 'both' and 'all'

What is the difference, or when and why should I use the definite article? E.g:
in all the three countries .... vs in all three countries...
both the countries were represented... vs both countries were represented...

Thanks

Maren

Try this link. Articles in English or "Charlie the Brave" / ESL Lesson
It's easy and clear.

Thanks, aous32, for the link. Unfortunately, the article explains the basic usage of articles, but says nothing about the particular case.
I'm still in need of explanation, as I know that both the usages (with and without the definite article) are right.

I think you can use "both the three countries" if these countries were already mentioned (I meant if the reader is expected to identify these countries, because they've been mentioned before or because it's clear in the situation where it occured)

hi,
I think that 'in all three countries' is rather informal, spoken form of 'in all the three countries'.
As to the second pair of sentences, I think 'Both the countries...' is rather awkward if not incorrect.