Answer:
In the case of Walter in "Breaking Bad," the police's desperation for an arrest did play a role in how they ultimately caught him.
Initially, Walter's activities as a methamphetamine manufacturer and dealer went unnoticed by the police. However, as Walter's criminal activities continued to grow, the Drug Enforcement Administration (DEA) began to investigate the local methamphetamine trade more aggressively.
As the investigation progressed, the DEA became increasingly desperate to make an arrest and dismantle the drug operation. One of the DEA agents, Hank Schrader, became fixated on tracking down the elusive drug kingpin known as "Heisenberg," who was responsible for producing and distributing high-quality methamphetamine throughout the region.
Eventually, Hank was able to connect the blue methamphetamine found at various crime scenes to Walter's unique production methods, leading him to suspect that Walter was Heisenberg. Hank's desperation to make an arrest and prove his theory ultimately led him to put together the pieces of the puzzle and finally identify Walter as Heisenberg.
So, in short, the police's desperation for an arrest did play a role in how they ultimately caught Walter. However, it was not the sole factor, as Walter's own actions and decisions also played a significant role in his downfall.