Assuming the software doesn't blow up (I'm not real confident, but with so much riding on it they might actually get it right this time), the Segwit2X folks should have SW enabled for signaling on July 21. With 86% miner support at the moment, IF some of the miners don't pull out at the last minute (i.e., Bitmain) then SW will be close to activation on August 1.
Note that this depends on a couple things. I'd put the chances of SW2X pulling it off at around 60%, IMO.
If something goes wrong or Bitmain reneges again, then BIP148 gets activated. It will be messy but it will win. Jimmy Song has a good article explaining why, and the case has only gotten stronger since he wrote it. The majority of miners, having just spent a month publicly declaring their intention to support SW, are not going to universally turn against it on August 1. Even if some follow Bitmain's lead or get cold feet, enough will stick with it to make BIP148 viable. And if it is viable on August 1, victory is virtually assured.
Song's article:
https://medium.com/@jimmysong/uasf-bip148-scenarios-and-game-theory-9530336d953eSo my prediction at this point looks something like this:
60% of Segwit activating thru SW2X, no BIP148 activation.
35% of Segwit activating though BIP148 w. some turmoil. Bitmain may try to fight with their planned fork, or may abandon its bluff. Doesn't matter either way.
5% of something else...