Simply put, the water leakage is caused by a buildup that’s blocking the normal draining of the drain line. This typically means the defrost line cannot channel away water appropriately, so the water must find some route of escape -- in this case, near the gap of the fridge’s bulb placement.
Depending on the amount of groceries you have in the fridge, you’ll need to clear out everything, including the freezer, to allow for better warm air circulation. Pack a cooler or ice chest with ice since this method is based on the amount of time perishables spend in warmer temperatures. Leave the doors of the freezer and fridge open for several hours. Lay some towels across the floor around the fridge to sop up excess drainage. Over time, circulating warm air melts the blockage to solve the problem. If this method doesn’t work, it’s time to roll up your sleeves and get to work.
After removing all contents of the fridge and freezer (again) and unplugging the unit from the wall, it’s time for some basic disassembly. Depending the model of your fridge, you’ll need to remove the actual bottom of the fridge from the inside; for other models, this may mean removing back wall of the fridge’s interior to give you direct access to the clogged line. If you don’t know the exact location or what you’re looking for, consult the manual included with your fridge. Chip away at any buildup accumulated on the underside of the removed panels. If you can see the ice buildup in the line, soak the line in a bucket of warm (not hot) water to melt it down.
Buildup and leaks are fairly common -- nothing to be too overly concerned about and no reason to run out and buy another unit. A proactive approach usually reduces the instance of buildup. Regular defrosting of the fridge or ensuring the defrost mode is set to a regular cycle helps reduce future mishaps.