The hardest part about a problem like this is figuring out what you actually mean.
The setup it sounds like you are trying to describe is this:
- You have a collection of statements $F_i$ -- the "facts" you know
- You have a statement $H$ -- the "truth" you are trying to learn about
- $P(F_i) = 0.51$ -- the probability of any particular fact being true is 51%
- All of the $F_i$ are independent
- If any $F_i$ is false, then $H$ is false too.
From this, you can deduce that if you have $n$ "facts", then $P(H) \leq 0.51^n$. An intuitive interpretation is that each $F_i$ you add to your repository of knowledge is evidence against $H$: you are collecting many, independent ways in which $H$ could fail, and each way has a 49% chance of actually happening.
It's probable that this isn't really what you meant. Maybe you meant something like $P(F_i | H) = 0.51$ -- that is, "if $H$ is true, then $F_i$ will be true with 51% probability".
In some sense, each $F_i$ you collect is evidence for $H$, and each $F_i$ that turns out to be false is evidence against $H$, but this really doesn't make sense in isolation. One way for it to make sense is when you're comparing $H$ against some other hypothesis $H'$, in which case you can make sense of the rate at which the evidence favors $H$ versus $H'$.
In particular, if you had $P(F_i | H') = 0.5$, then each $F_i$ you see that's true would tilt things slightly in favor of $H$, and each one that's false would tilt things slightly in favor of $H'$. If you get a lot more $F$'s that are true than false, then this can accumulate to a lot of evidence favoring $H$ over $H'$. Of course, if you get too many true $F$'s, you should strongly suspect tampering with the data or severe errors in your model.
If there were some other set of facts $G_j$ such that $P(G_j | H) = 0.9$ and $P(G_j | H') = 0.5$, then discovering $G_j$'s would rapidly accrue evidence in favor of $H$, but each one you find that turns out false would be a severe blow against $H$.
Whether looking for $F$'s instead of $G$'s is better overall in distinguishing between $H$ and $H'$ would depend very much on how many of each you get to look at.