Emission probability in blackbody spectrum derivation

[Swamp Thing]

This clip refers to an emission probability p. Would this be a probability density (probability per unit time)? The presenter doesn't emphasize this, but I would like to make sure whether that is the case.

https://youtube.com/clip/UgkxxP5JQkuMJ62AVyDKdm6ixJFBVrT1-l7a?si=icaigJovcG5qg83l

 

[Demystifier]

No, $p$ is not probability density. It's just the probability that emission happened.