"In the big countries" when you have specific big countries in mind (because of a definite article)
"In big countries" when you speak about any big countries   (if this part of a sentence was written in a singular form - In a big country - there would be an indefinite article. In the plural, the indefinite article is omitted)

I wonder what it's like to live in the big countries (US, Canada, Brazil, Russia, etc)
I wonder what it's like to live in big countries (in general, with no specific countries in mind)

Hey Sara:)

Well, I think the is not required in this sentence as "In big countries" is right.

But "the" is relevant if you write--Russia is the biggest country(before the superlative degree) or before those countries whose name includes words like--Kingdom,States or Republic  Or countries which have plural nouns as their names like--the Netherlands; the Philippines.

Please correct me If I'm wrong.Thank you:)