Stop water pooling on a shower pocket shelf?
Short of taking the shelf up (which might not be possible depending on the relationship of the shelf to the wall stone, and will probably be difficult in any case) you are going to need to cut channels into the surface, as it has been (improperly, by my lights) installed flat, rather than properly sloped to drain.

If you can get the shelf out intact (or not intact, and you get a replacement) you can shape the mortar bed to let the shelf self-drain without surface cuts.

Fortunately marble is pretty easy to cut channels into, as stone or tile goes. Granite or porcelain tile would be a lot more difficult to modify in this way. Make sure that the channels are angled to drain (deep on the shower side, shallow towards the rear.)