I have a kenmoore fridge that is dripping water from the top side of the fridge compartment (traditional freezer on top style). It appears to be coming from an assembly containing a plastic (condensate?) hose that runs down the middle of the "ceiling" of the fridge compartment and drips near the rear of the assembly where the hose runs. Currently, I have a cup under it which also seems to freeze at times.

Any tips on DIY repairs would be great as I am not one to quickly dive into appliance repair, but would like to save a few bucks if possible.

Thanks in advance.