How do I determine the path to a binary of a process?

The /proc way would be to inspect the exe link in the directory corresponding to the pid.

Let's take an example with update-notifier:

Find the pid, which is 15421 in this example:

egil@gud:~$ ps x | grep update-notifier
 2405 pts/4    S+     0:00 grep update-notifier
15421 ?        Sl     0:00 update-notifier

Look up the symbolic link:

egil@gud:~$ file /proc/15421/exe
/proc/15421/exe: symbolic link to `/usr/bin/update-notifier'

Maybe which is what you are looking for. For instance, on my system

which firefox 

returns

/usr/bin/firefox

See also Find Path of Application Running on Solaris, Ubuntu, Suse or Redhat Linux .

Providing you've a process ID available, you can use:

readlink -f /proc/$pid/exe

(replace $pid by the process ID of a process)

If the process is not owned by you, you'll have to put sudo in front of it.

An example for determining the location of the command firefox:

1. The output of ps ax -o pid,cmd | grep firefox :

   22831 grep --color=auto firefox
   28179 /usr/lib/firefox-4.0.1/firefox-bin
   

2. 28179 is the process ID, so you've to run:

   readlink -f /proc/28179/exe
   

   which outputs:

   /usr/bin/firefox