What are the chances of each gumball dropping?

Every time you touch the handle, the game rolls a random chance from this list:

• Bumper (Black): 4 out of 16
• Ring (Grey): 2 out of 16
• Clear (Nothing): 2 out of 16
• Water Shield (Blue) : 2 out of 16
• Flame Shield (Red): 2 out of 16
• Electric Shield (Orange): 2 out of 16
• Rep (Green): 1 out of 16
• 1UP (Pink): 1 out of 16

source for this list is http://hcstealth.tumblr.com/post/100311283757/sonic-3-knuckles-20th-anniversary

The Rep chances are unique in that if the game rolls a Rep while the bottom springs are still active, the game will re-roll that particular chance using a different list:

• Black (Bumper): 8 out of 16
• Clear (Nothing): 4 out of 16
• Ring (Grey): 3 out of 16
• 1UP (Pink): 1 out of 16

The game also checks the result of the roll against its last roll, and if the result would be the same, it "flips a coin" on whether or not the result is re-rolled.