I was assuming Charlie would show Bob the first person to see 75⁄100.
Anyway, your analysis solves this as well. Being the first to see a particular result tells you essentially nothing about the composition of the pond (provided N_sci is sufficiently large that someone or other was nearly certain to see the result). Thus, each of Al and Bob should regard their previous observations as irrelevant once they learn that they were the first to get those results. Thus, they should just stick with their priors and be 50⁄50 about the composition of the pond.
I was assuming Charlie would show Bob the first person to see 75⁄100.
Anyway, your analysis solves this as well. Being the first to see a particular result tells you essentially nothing about the composition of the pond (provided N_sci is sufficiently large that someone or other was nearly certain to see the result). Thus, each of Al and Bob should regard their previous observations as irrelevant once they learn that they were the first to get those results. Thus, they should just stick with their priors and be 50⁄50 about the composition of the pond.