I believe you can condition on a probability of proposition.
For example, if you are in a fairly dark room and you observe with 90% confidence a red object.
Then you can do (iirc)
P(X | 90% confidence see red object) = 90% * P(X | see red object) + 10% * P(X | do not see red object)
I would think that in principle, this allows for allowing all observations to be fallible, without any kind of “infinite regress” problem? You just apply the same kind of process each time.