use File::Spec::Functions qw/abs2rel/;
my $path = "C:\\Dir1\\Dir2\\Dir3\\KeepMe";
my $base = "C:\\Dir1\\Dir2\\Dir3";
print abs2rel($path, $base), "\n";  # prints "KeepMe"
# - or -
use Path::Class qw/dir file/;
my $path = dir('C:\\','Dir1','Dir2','Dir3','KeepMe');
my $base = dir('C:\\','Dir1','Dir2','Dir3');
print $path->relative($base), "\n";  # prints "KeepMe"