What is the probability of forking in blockchain?
Actually, it is not related to the difficulty at all, rather just related to the expected time until the next block is found.

Block finding is a Poisson process.

The probability of x blocks occuring in the amount of time we'd expect λ blocks occuring therefore is:  


  


In ideal conditions, we expect one block per ten minutes, i.e. 600 seconds. Therefore in 2 seconds we'd expect 1/300 blocks occuring.

p(2|1/300) evaluates to approximately 5.54*10-6 which is about 0.000554%, i.e. we'd expect two blocks to occur within two seconds once every 180k blocks or every ~3.4 years.

More exciting are ten seconds which has a probability of about 0.00014, i.e. we'd expect two blocks within ten seconds to happen once every 7000 blocks, i.e. roughly every seven weeks.