Client sues attorneys for legal malpractice, and attorneys counterclaim against client for "contribution and indemnity." When may this properly go forward? What is "contribution" and what is "indemnity" ?

Contribution is the apportionment of fault among joint tortfeasors. Several contractors who each negligently damage a tenant might seek contribution among themselves.

Indemnity is the situation

A French artist wants to buy an apartment in New York for a studio and living space. So far, this could be the start of a fairy tale in which the artist comes to NY, works hard, triumphs, etc. But, this real estate transaction soon turned to legal malpractice litigation. One reason for the problems