In this paper, I provide a probabilistic account of factual knowledge, based on the notion of chance, which is a function of an event (or a fact — I will use ‘fact’ to cover both) given a prior history. This account has some affinity with my chance account of token causation, but it neither relies on it nor presupposes it. Here, I concentrate on the core cases of perceptual knowledge and of knowledge by memory (based on perception). (The account can be extended to the other modes of knowledge, but not in this paper.) The analysis of knowledge presented below is externalist. The underlying intuition guiding the treatment of knowledge in this paper is that knowledge boils down to high token discriminative indicativeness. Type indicativeness or type discriminability are neither necessary nor sufficient for knowledge: the token aspect comes out in the strong dependence on the specific circumstances and chances of the case. The main condition of the first section, the indicativity condition (KI), properly refined, yields pertinent (token) indicativity as a main constituent. Very roughly, it involves the chance of the content clause p being higher given the subject's believing that p than otherwise. The discriminability condition in question (section 3) captures the sense of discriminability appropriate for knowledge and yield the indicativity condition: it is an extension of the indicativity condition KI. Roughly, the subject’s ability to discriminate the object in front of her being red from its being green is captured by holding fixed, in the indicativity condition, the condition “the object in front of her is red or green.” A major element in the analysis is the so-called Contrast Class, which governs the scope of discriminability. This is the class of features that have to be taken into account in the discriminability condition, and it is characterized by two constraints. Very roughly, according to the first constraint, for a feature to be in the contrast class, it must not represent a sub-type of (the feature specified by) the predicate in the content clause. According to the second constraint, which is a central condition with many implications, the chance that the object specified in the content clause has a feature represented in the contrast class must not under the circumstances be too low. This constraint, within the framework of the discriminability condition, brings out a major constitutive aspect of knowledge: knowledge amounts to a limited vulnerability to mistakes of the belief in question under the circumstances at hand. The contrast class plays a major role in my treatment of skepticism. The second constraint on the Contrast Class together with the VHP condition below bring out precisely the way in which perceptual knowledge is fallible.