How can we justify the inference from observed instances to unobserved instances, or from past experiences to future predictions, without circular reasoning?
When two things correlate there are four possible relationships;
a, b) one caused the other
c) they share a cause
d) they correlated arbitrarily
Three of those are causal, therefore in lieu of other evidence, you are 3x as likely to be correct to assume they will continue to relate causally similarly under similar conditions in the future.
Even before replication, whatever 100% of evidence supports, empirical or logical, however minimal, is sufficient for 51% certainty in absence of any evidence to the contrary.
In simple terms, the evidence of the past is all we have by which to judge the likelihood of the way things will continue to work. Even if such a belief turns out to be wrong, we still had epistemological certainty before that new evidence was available.