When. Among the morning and evening remembrances, said while healthy. That is the whole shape of it: refuge is sought before there is anything to seek refuge from, in the way a person insures a house that has not burned.
The words. Three named conditions and then a closing sweep. Al-baras and al-judham are diseases of the skin and the body's visible surface, the kind that alter how a person is seen and how near others will come. Al-junun shares a root with jinn, the concealed — its sense is a mind covered over, hidden from itself. Then sayyi' al-asqam: saqam is not the general word for illness but the settled, chronic kind that a body carries for years, and sayyi' qualifies it as the worst of that kind. The list moves from the specific to the open-ended so that nothing is left out by having been forgotten.
Why these three. They are not the fastest killers, and that is the point. What the three share is isolation — two of them change the face and the skin until people stand further away, and the third removes a person from himself. The supplication is about being cut off, not merely about pain.
Naming them is not contempt. Asking to be spared a condition says nothing against those who live with it. Trials are distributed without reference to worth, and the one asking for refuge today is the one who may be visited tomorrow. Nothing in these words licenses recoiling from a sick person.
The other side of it. It has a natural counterpart in the practice of thanking Allah for wellbeing on seeing someone afflicted — the same subject approached from safety rather than from fear.