A paradox in the philosophy of confirmation. Suppose a hypothesis is assigned a quite low or quite high probability given some body of evidence. Then in principle more evidence might be found confirming that assignment. What is the difference this evidence makes? On the one hand the low or high probability stays the same; on the other hand such evidence seems, intuitively, to make confidence in the hypothesis more irrational, i.e. to lower its probability, if it is already low, or to make confidence in the hypothesis better founded, i.e. to raise its probability, if it is already high. The problem is that weightier evidence justifying an existing low or high assignment of probability seems to have something of the effect of evidence in favour of a yet lower or higher probability.