OK, I couldn't find any sites that told the exact percentage for reeling a Pokemon, so I did a survey, the following are the results.
When just normally fishing, I fished 50 times. 34 times I reeled a Pokemon, and 16 times I didn't. Then I times them both by 2 to get it out of 100.
34 x 2 = 68
16 x 2 = 32
Now that it is out of 100, we can see that as Gligurr said it is around 69%, so around 70%.
Next is for fishing near a rock. I also fished 50 times for this and out of 50 I reeled a Pokemon every time.
This means that fishing close to a rock has a 100% chance to reel a Pokemon, or at least very close at around 97% or something like that. this means you don't need a Suction Cups Pokemon to chain fish.
I can't give any exact percentages, but this is probably accurate.
Hope I helped!
Source: The above surveys