Halliday & Matthiessen (2014: 537):
The first three differ in terms of modality of the subtype modalisation:(1) cases (nouns of simple fact) relate to ordinary non-modalised propositions ‘it is (the case) that ... ’
(2) chances (nouns of modality) relate to modalised propositions ‘it may be (the case) that ... ’
(3) proofs (nouns of indication) relate to propositions with indications, which are equivalent to caused modalities, ‘this proves/implies (i.e. makes it certain/probable) that ... ’