From what I understand, you're asking if the gacha rolls like this:
3% chance to get SSR -> P(SSR)=0.03
15% chance to get the boosted SSR (?) -> P(boosted|SSR)= 0.03*0.15 =0.0045
25% probability to get one out of 4 (?) -> P(Actual hime|boosted|SSR)= 0.0045*0.25 = 0.001125
Mathematical notation: The probability of getting a boosted hime out of the 4 SSRs that exist in the list, given that your roll actually is an SSR.
My answer is... I don't know. If what you're saying is indeed correct, the above calculations probably apply that way, but like Sana has mentioned, I'm not sure how you've obtained your 15% and 25% to begin with.
But from an RNG gameplay perspective, I prefer applying Murphy's Law, and therefore will always pick the calculations that gives me the lowest probability since I'm biased in my view of gaming RNG
Either that, or apply Slashley's pet phrase: RNG is gonna RNG you no matter what.