DES - Weakness in Sbox
The attack on 3 rounds is deterministic. It is extended to 4 rounds in a probabilistic manner, which is the normal way of carrying out differential cryptanalysis, see for example Heys' tutorial on linear and differential cryptanalysis which is easy to find online and uses a simple toy cipher to explain these concepts.

Basically, given enough input output pairs, one can use the fact that those differences will statistically dominate. Scan through a set of subkey bit patterns and declare the subkey bit pattern which leads to the most biased output difference distribution as the correct key bit pattern.