Batman/The Shadow: The Murder Geniuses
While investigating the murde of a Gothamite, Batman identifies his prime suspect as Lamont Cranston... but there are two problems with that. One, Batman is not aware Lamont's alter ego is the master detective known as the Shadow. Two, and more importantly, Cranston seems to have died over half a century ago!
Collects BATMAN/THE SHADOW #1-6 and stories from BATMAN ANNUAL #1.