How likely is the contraction of aids from getting aids blood on a cut?

Depends on situation: If blood from an HIV positive person contacts a cut on another person, the likelihood of transmission would depend on many factors, such as: volume of blood in exposure, viral load of the infected patient, nature of the wound (healing with an intact scab/crust versus open wound), duration of contact and immediate cleansing versus not... If low viral load and minimal splash, then limited risk...