But we can't possibly have any knowledge other than that which we observe or derive from our experiences.  Furthermore, even though our initial perceptions may not accurately represent reality, I've never seen any reason to suspect that they don't follow a consistent and useful cause-and-effect behavior model.  A few examples:

* When I look around I perceive physical objects around me which appear to have colors, textures etc.  Scientific experiments and tools have demonstrated that there's more to these objects than what I can perceive just by casually looking at them, but nothing about that suggests that my perceptions aren't the systematic result of a useful process for perceiving relevant differences in those physical objects.  My computer looks and feels different from my couch, and I have no reason to suspect that those differences in my perceptions do not accurately illustrate differences in the actual materials.

* When I dream or daydream, I can experience things that I wouldn't necessarily be able to experience while I'm awake.  However, I appear to be able to consistently identify which of my experiences are dreams and which are not by virtue of a certain quality of awareness which I'll attempt to explain here.  When I'm dreaming or daydreaming, everything in the dream is created by my mind, and therefore I have a certain awareness of every dream element that I don't have when I'm awake and perceiving the real world.  In the real world, I'm aware only of what I can perceive through observation.  Also, my dreams don't seem to be constrained by the same physical limitations that my experiences when awake seem to be.  Furthermore, my dreams seem to deal with things that I've experienced or thought about in ways that seem to have a logic all their own, so even within dreams I suspect that my perceptions are still the result of some underlying deterministic mechanism(s).

* While I don't have any experience with hallucinogenic drugs, I do have the consistent experience of not hallucinating while not taking hallucinogenic drugs, so I can confidently deduce that any inconsistencies with those perceptions and an objectively reality could be attributed to those drugs.

And, while it's true that I can't be sure exactly what the underlying causes of my perceptions are... that is to say, I can't be certain I'm not plugged into The Matrix or that I'm just a brain in a vat being fed neural impulses by some system which monitors my own thoughts and generates a complex and consistent illusionary world... in real time... that doesn't really matter.  Since I have no way of being more certain about whether or not that I'm observing an objective, unfabricated reality than I currently am, it's epistemologically justifiable to assign that level of confidence as 100% and use it as the standard for which confidence in other propositions can be measured against.

Well, there is a certain problem with this.  You can have a lifetime of experiences which indicate, as a pattern, that a certain law of nature exists where in fact that law doesn't exist, or at least doesn't exist in the manner in which your experiences lead you to believe it does.  For example, the scientific discovery has been made that water can transition directly from a solid to a gas and vice versa under certain combinations of temperature and pressure.  However, prior to that discovery, it's reasonable to assume that most people would live their entire life never seeing such a phase change in water and might reasonably assume that such a phase change cannot happen, and that water must pass through a liquid state when transitioning from a solid to a gas or vice versa.  Given our current knowledge and the state of modern science, we can look back and see that such a conclusion would not be true and therefore couldn't be called knowledge.  Therefore, we must conclude that the method by which such a person would arrive at that conclusion is not sufficient to determine knowledge, i.e. does not constitute proof.

The problem with basing beliefs on probabilities is that probabilities are assigned based on current knowledge and beliefs.  If I flip a coin, I would assign a roughly equal probability that it will land with one side up versus the other.  However, an omniscient observer would be able to determine, based on superior knowledge, exactly what the result would be with 100% certainty.  So the probability of the outcome is not an inherent and objective property of the event, but rather is as estimate of the likelihood of any given outcome based on currently available limited knowledge.

Essentially, probability is an expression of confidence in a proposition rather than an objective observation... it is the end-product of epistemological study rather than a tool to be used in an epistemological investigation.  However, it is worth noting that because we build knowledge upon other knowledge, it may be useful to take an assigned probability of one proposition and use it to help determine justifiable confidence in another proposition (which may be what Hambydammit was trying to say).  Exactly how such compound assessments of probability should be handled is, perhaps, a worthy topic for epistemological debate.