Alright lets do some calculations. Feel free to dissect the assumptions.
K event = Kim says Material L is RTSC
D event = DFT says L is RTSC
S event = L is actually RTSC
we have assumed P(S/K) and P(S/D) are each 0.1, though we could have chosen other numbers for them as well.
We want to estimate P = P(S/(K and D))
P = P((K and D)/S)P(S)/P(K and D)
Assuming Kim and DFT are in the business of making positive predictions, they always get it right when L is actually RTSC.
so P(K/S),P(D/S) and P((K and D)/S) are all taken as 1
hence P = P(S)/P(K and D) = P(S)/(P(K)P(D/K))
= P(S/K)/P(D/K) = 0.1/P(D/K)
(similarly, P = P(S/D)/P(K/D) = 0.1/P(K/D))
But ofcourse we dont know P(D/K) or P(K/D). We could check historical data on how often D aligns with K, a messy exercise at best. Say they dont perfectly align, then the conditionals are less than 1,and P>0.1. Even intuitively when K (or D) gets additional support in the form of D (or K), your P should increase, not decrease.
If we assume D and K align on average, then P(D/K) or P(K/D) is 0.5, and we get P = 0.2.
You may estimate everything above differently, thus getting a different P. You can also come up with your own way of modelling this. I came up with my particular estimate to understand how frequently should i follow the news, and care about the whole thing. You should model it according to your usecase.