I sent a ticket to Nutaku Game Support (Kamihime Project R, sub-category Gatcha), reading as follows:
Could you provide a breakdown of the likelihood of drawing a kamihime vs. a weapon with no kamihime vs. an eidolon in the Premium Gatcha? If it varies by rarity (R, SR, SSR), then please provide the rates for SSR.

I intend to share this response publicly to inform users considering spending on Premium Gatcha. Thank you for taking the time to respond to this important question.