Slowing 60fps footage for a 24fps timeline

As Mylenium said, you have a couple of options. There are three icons at the bottom left corner of the Timeline panel. The third looks like this {}. That one will bring up the In/Out/Duration/Stretch column where you can retime any footage. 

You can apply Layer/Time/Time Remapping and slide around the keyframes that are generated, set new ones, and use the Graph Editor set to Speed to visualize the percentage of real-time right in the graph. The values are in seconds per second, so sliding the keyframe around until you hit .4 will give you a 40% reduction in real-time.

Playback speed is also controlled by footage interpolation. You access that from the Project panel by selecting the footage and then using the File/Interpret Footage menu or the shortcut Alt/Option + Ctrl/Cmnd + G. If the footage was shot at 60fps and you want to slow it down by 40% multiply the frame original frame rate by .4. You can do the math right in the Conform Frame rate panel by typing 60 * .4.  That's all there is to it.  I almost always use footage Interpolation when I am fiddling with playback time as a first step.

The composition frame rate has nothing at all to do with playback speed.  The only way to have composition frame rate affect the playback speed of a layer is to multiply a Time Remapping expression by thisComp.frameRate. That's the only way I can think of to make the composition's frame rate change the playback speed of a layer in the timeline.

I'm not clear what you are asking. You can dial in those exact 40% in Timewarp or by using time-remapping. Otherwise you would simply re-interpret your 60 FPS footage as 24 FPS in the footage interpretation to force it to display every frame.

Mylenium