Probability of finding a particle in a solid angle

[cjurban]

I have an interesting question that I'm not sure how to go about solving. This question has a little general relativity and (maybe) a little QM, but I wasn't sure where to post it.

Question:
Imagine that a [itex]\pi[/itex]⁰ meson traveling along the z-axis (velocity v=0.99c, rest mass M) decays into two photons. The angular distribution of the photons is isotropic in the rest frame of the pion. If in the lab frame the [itex]\pi[/itex]⁰ meson travels with velocity v in the z direction, what is the probability P(θ)dΩ that a photon is emitted into the solid angle dΩ?
We also know [itex]\int[/itex]P(θ)dΩ=1.

My ideas:
I know the Lorentz transformations, so switching between frames is no biggie. I know Ω[itex]\equiv[/itex]A/r², and I know the differential solid angle. What's confusing to me is P(θ). Do I need to get the particle's wave function, as in P(θ)=ψ²(θ)? How would one do this? Any hints would be helpful.

 

[dauto]

The probability P(θ) dθ that the particle is between θ and (θ + dθ) will be the same probability P'(θ') dθ' that the particle is between θ' and (θ' + dθ'), where θ and θ' are the angles as measure in the two different reference frames (Aberration formula). Since P(θ) is known, it is possible to calculate P'(θ').

 

[cjurban]

P(θ) is known? Am I missing it? I'm not exactly sure what it would be, or how to get it.

 

[dauto]

Didn't you say the distribution is isotropic in the rest referential frame? P(θ) must be inversely proportional to sin(θ) and the constant of proportionality is found by normalizing the probability