There are two ways to study price in ACBC:
1) Standard independent attribute
2) Summed pricing attribute (semi-correlated with other product attributes)
If you use option #1 and wanted 1/4 of the time that the price is $0, then you could create 4 attribute levels for price:
Level 1: $0
Level 2: $20
Level 3: $40
Level 4: $60
You would select to DROP the price attribute from the BYO section, as it would be strange to ask respondents which level they prefer of price. Of course, each of these 4 levels of price would have 25% likelihood of being shown, since when dropping price from the BYO section, we sample equally across the levels.
If you use option #2, you don't have any control what % of the time the $0 is shown at. You would specify that price is "summed" based on other attribute levels, and then "shocked" by typically a +/-30% interval. You assign price increments to other price levels such that more capable "products" are typically shown at higher prices on average.