This is something you have to tell your OS to do. In Windows, for example, you would do this by right-clicking a .dfg file, selecting the "Open With -> Choose Program..." choice, picking your exported Processing application as the program to use to open it, and then checking the "Always use the selected program to open this kind of file" check box.

No this is not what i mean (because i know how to do this and its beter in registry but this is not the them of my post). What i mean is can processing know that it's program has been open by external file and get hits path ?

Well, it looks like this is highly dependent on the application itself. If I open an image in a file viewer, there is no obvious way to see its path, unless opening the dialog showing the properties of the image (if any).
Or you need to access the program' system image, to get the command line used to run the application. Something system-dependent, so Java (thus Processing) isn't a good fit for such low level operation.