If your case is that simple (exactly one / in the string) use split_part():
SELECT split_part(source_path, '/', 2) ...
If there can be multiple /, and you want the string after the last one, a simple and fast solution would be to process the string backwards with reverse(), take the first part, and reverse() again:
SELECT reverse(split_part(reverse(source_path), '/', 1)) ...
Or you could use the more versatile (and more expensive) substring() with a regular expression:
SELECT substring(source_path, '[^/]*$') ...
Explanation:
[...] .. encloses a list of characters to form a character class.
[^...] .. if the list starts with ^ it's the inversion (all characters not in the list).
* .. quantifier for 0-n times.
$ .. anchor to end of string.
db<>fiddle here
Old sqlfiddle