Some arbitration with other markets:

P(win|!Biden) = P(win) \* P(!Biden|win) / P(!Biden)
= P(win) \* (1 - P(Biden|win)) / (1 - P(Biden))
= P(win) \* (1 - P(win AND Biden) / P(win)) / (1 - P(Biden))

= P(win) \* P(win AND Biden) / (1 - P(Biden))

= https://manifold.markets/MuhammadImran/will-democrats-win-the-us-2024-elec \* (https://manifold.markets/MartinRandall/will-joe-biden-win-the-2024-preside OR https://manifold.markets/LarsDoucet/will-joe-biden-win-the-2024-us-pres) / (1 - https://manifold.markets/NathanpmYoung/will-biden-be-the-2024-democratic-n)
= 0.68 * 0.50 / 0.70

= 0.48

If you think this is wrong, you might want to bet on the P(win) market, since that has only had a few betters so far

P(win AND Biden) = https://manifold.markets/MartinRandall/will-joe-biden-win-the-2024-preside = 0.50
P(win) = https://manifold.markets/MuhammadImran/will-democrats-win-the-us-2024-elec = 0.68 (low confidence)
P(Biden) = https://manifold.markets/NathanpmYoung/will-biden-be-the-2024-democratic-n = 0.70

(The reason for the \* in the above comment is that if you try to write two asterisks otherwise, they disappear and make the content between them italicized)