There are two things to consider here:
1) The content of the executable file is likely kept in the OS cache (disk cache). While that data is still in the OS cache, every read for that data will hit the cache and the OS will honor the request without needing to re-read the file from disk
2) When a process exits, the OS unmaps every memory page mapped to a file, frees any memory (in general, releases every resource allocated by the process, including other resources, such as sockets, and so on). Strictly speaking, the physical memory may be zeroed, but not quite required (still, the security level of the OS may require to zero a page that is not used anymore - probably Windows NT, 2K, XP, etc, do that - see this Does Windows clear memory pages?). Another invocation of the same executable will create a brand new process which will map the same file in the memory, but the first access to those pages will still trigger page faults because, in the end, it is a new process, a different memory mapping. So yes, the page faults occur, but they are a lot cheaper for the second instance of the same executable compared to the first.
Of course, this is only about the read-only parts of the executable (the segments/modules containing the code and read-only data).
One may consider another scenario: forking. In this case, every page is marked as copy-on-write. When the first write occurs on each memory page, a hardware exception is triggered and intercepted by the OS memory manager. The OS determines if the page in question is allowed to be written (eg: if it is the stack, heap or any writable page in general) and if so, it allocates memory and copies the original content before allowing the process to modify the page - in order to preserve the original data in the other process. And yes, there is still another case - shared memory, where the exact physical memory is mapped to two or more processes. In this case, the copy-on-write flag is, of course, not set on the memory pages.
Hope this clarifies what is going on with the memory pages.