Thank you. It' clear, now.
In English-Turkish dictionaries "sob" means only "hiccup". And I though that convulsive gasp made in weeping fitted to it, because "hiccup" (not "sob") is associated with crying in Turkish.
Then, as you can imagine, "hiccup of relief" didn't make any sense.
A last question: Can I use "a huff of relief" in the same sentence for the same context?