I’m new to this software as of just a few days ago, and things were going fine until I needed to use probability and couldn’t figure out how. I’ve figured out the randomize blocks feature, but I’m having trouble changing it so that one tile is more common than the others. I had previously downloaded a much older version of Tiled in which all I needed to do was select the probability and change the number, but for some reason in this newer version the probability (and all of the other things on that side bar for that matter) are ‘greyed out.’ I can’t interact with them. 
Indeed tile properties are displayed as read-only while you’re editing the map. The tile probability is stored in the tileset, and to change things affecting the tileset you first need open that tileset. This is briefly mentioned in the manual page about Editing Tilesets, but unfortunately it’s rather unintuitive.
This is something that changed in Tiled 1.0, because since then tilesets are edited separately (before Tiled 1.0, editing of tilesets always happened as part of the map and external tilesets weren’t very well supported - they could only be edited when they were (temporarily) embedded in the map).