You COULD use a central server, or set one of the 3 servers as the shared respository for all files, but that is going to cause unnecessary network overhead and also reintroduce a single point of failure.
A better method would be to implement a set of scripts that would keep the servers in sync.
Rsync can be used for this, but there are any number of options including using git. (You DO use source code management right?)
Capistrano is also a good option.
Also see answers here: Deploying to multiple servers