I am writing a paper for a conference. I have finished the paper, but I must review some experimental results and this requires some additional days.
How can I find out the probability that the submission deadline will be extended?
Just look at past editions and see if there was indeed an extension. If they always do it, there will be another one; if they never extend, there is no reason to believe they will start this year.
If they don't, you could always give a shot to a polite email to the organizers and explain your situation. Perhaps you can submit a tentative proposal, with the uncertain data, and submit a refined version later (provided it doesn't change much).