New information is allowed to make a hypothesis more likely, but not predictably so; if all ways the experiment could come out make the hypothesis more likely, then you should already be finding it more likely than you do. The same thing is true even if only one result would make the hypothesis more likely, but the other would leave your probability estimate exactly unchanged.

One result might change my probability estimate by less than my current imprecision/uncertainty/rounding error in stating said estimate. If the coin comes up H,H,H,H,H,H,T,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H... then I can assign a low probability to it being fair, but a lower probability to it having two heads.