Menu block doesn't appears where I expect it
Solved that! Inspecting the code of Menu Block cleared it out for me that this module doesn't work with URLs. What a pity!

But: 

There is a completely awesome bunch of modules: Context withContext:Menu Block which make it possible.
Context menu block modules make Menu Block module being aware of context. Also this page may be useful.

But still, if you have better solutions, please write it here.