Leur pouce vs Le/La/Les pouce

Question

Elsewhere on the site, there is an example sentence: Ils sucent encore leur pouce. They're still sucking their thumbs.  Why doesn't leur pouce become le/la/les pouce(s)?

Accepted Answer

In French you say: ils sucent leur pouce, using singular for le pouce, because each one is sucking only one thumb. If you said ils sucent leurs pouces, it would mean that each one was sucking more than one thumb.
This is different from English, where you look at all of them as a group, in which case there are more thumbs being sucked at once, even though each one is sucking only one thumb.

Answer

I’m not sure Chris’ answer answers the initial question, which I also have. Dhiraj is asking  why the “leur”, ie possessive, is used in that sentence, not les (or le), ie definite article?