Yes, like the latter scenario. Note that the expected utility of digging is low when the evidence against from one dig is low.
edit: Also. In the former case, not seeing a dragon sitting on your head is very strong evidence against there being a dragon. Unless you invoke un-testable invisible dragons which may be transparent to x-rays, let dust pass through it unaffected, and so on. In which case, I should have a very low likelihood of being convinced that there is a dragon on your head, if I know that the evidence against would be very weak.
edit2: Russel's teapot in the Kuiper belt is a better example still. When there can be only very weak evidence against it, the probability of encountering or discovering strong evidence in favour of it must be low also, making it not worth while to try to come up with evidence that there is a teapot in the Kuiper belt (due to low probability of success), even when the prior probability for the teapot is not very low.
Then, to extend the analogy: Imagine that digging has potentially negative utility as well as positive. I claim to have buried both a large number of nukes and a magical wand in the garden.
In order to motivate you to dig, you probably want some evidence of magical wands. In this context that would probably be recursively improving systems where, occasionally, local variations rapidly acquire super-dominance over their contemporaries when they reach some critical value. Evolution probably qualifies there - other bipedal frames with fingers aren't particular...
Another month has passed and here is a new rationality quotes thread. The usual rules are: