A more thorough explanation:

A writ of probable cause is a legal document that allows a prisoner to appeal the denial of federal habeas corpus relief. It is also known as a certificate of appealability (COA). The writ is issued by a United States circuit judge and certifies that the prisoner has shown that a constitutional right may have been denied.

For example, if a prisoner believes that their right to a fair trial was violated, they can file a writ of probable cause to appeal the denial of their habeas corpus petition. The judge will review the case and determine if there is enough evidence to suggest that a constitutional right may have been denied.

The prisoner does not have to prove that their case would succeed on the merits, only that reasonable jurists would find the claim at least debatable. If the certificate of appealability is not issued, no appeal is possible.

Overall, a writ of probable cause is an important legal tool that allows prisoners to appeal the denial of their habeas corpus petition and seek justice for potential violations of their constitutional rights.