For this to happen:
1) exchanges need to list the two bitcoins
2) users in the market need to prefer the segwit bitcoin over the original bitcoin and vote with their money, selling their original bitcoins, and buying segwit bitcoins in majority
Miners will follow with their hash rate.
Whenever the segwit chain overtakes the original chain, the original fork becomes orphaned (can be a month later) and all the transactions on it disappear in a puff.
Who will be brave enough to sell the original bitcoins?
Due to current high price of BTC miners do not have to sell all of their BTC to cover their operating cost. They will have a surplus and can dump their Bitcoins or Bitcoins seggy. Dump bitcoins then buy again low to create a majority again and hold even more BTCs. Dump BTC - seggy to make sure it stay a minority. I expect market manipulations to be the order of the day. The rest with few BTCs will be either panicking or closing their eyes and praying for the best. Thus hashrate may yo yo between Bitcoin and Bitcoin - seggy.
UASF could turn out brilliantly or equally disastrously.