If Lot went to Zoar, why did his daughters think no one was left on earth?

Did Lot actually go to Zoar? Bible text would suggest yes. However, why would the daughters think no one was left on earth? Genesis 19:31. It seems to me they arrived in Zoar and later left. Although it doesn’t indicate how long nevertheless I’m assuming there were people there.

Now, if they actually never got there it makes sense. However, Genesis 19:23 seems to suggest they did actually go to Zoar.