Dollars in a box

Suppose you're given a box, which contains either $1 or $5 (with equal probability). Then, an additional $1 bill is added into the box, and it's shaken up. To recap, you now have two bills total in your box, one is a known $1 bill, the other has a 50/50 chance of being a $1 bill/$5 bill.

Next, you randomly draw a bill from the box, and your draw turns out to be a $1 bill. If another person now comes and draws the remaining bill from the box, what is the probability that it is also a $1 bill?

You should be able to show your logic using conditional probability here.