one more thing:
i have looked inside ajax response and i see that value from bean is properly fetched and elements for hintDiv element Body replacement have been successfully prepared in response. But when requested elements are indeed present in ajax response, resulting html element is not updated. I don't know why
Does anybody have any idea what is wrong ?
Can't really tell, but maybe try putting hintDiv inside another div (which is always rendered) and reRender that new outside div instead.
If a div was not rendered do to the rendered attribute, you cannot reRender it. This has been stated multiple times in past threads.
reRender of conditionally rendered elements not allowed (nothing to update in DOM if the element isn't rendered initially). Define wrapper (outputPanel) and update just the wrapper component.