As you know, CAVOK is reported when visibility is greater than 10km (and cloud above 5,000 feet, not CB TCU etc). When vis falls below 10k, it is reported as such. When it falls below 5km the type of obscuration is additionally reported, eg BR, HZ, FU, IC, DU or SA (mist, haze, smoke, ice crystals, dust or sand).
The type of poor vis is important in a pilots assessment of how those conditions actually relate to his plan to continue the flight and how it relates to other conditions (eg early winter evening temp/dewpoint similarity and 3000m BR is a warning sign, Lagos in December during the Harmattan and a SA warning, Delhi in January at dinner time with FU in the METAR all help the experienced pilot build up a better image of what's happening, and likely to happen as they get near to the ground).
3km vis for people who are used to 100 mile vis can be quite alarming but still very workable as long as situational awareness and lookout is not compromised.