Rational Investigation; Fair Investigation; Due Process

You are an American trial lawyer or a police detective. You believe that Vila Victim is dead. You have five hypotheses -- H-1, H-2, H-3, H-4, and H-5 -- about how her death might have happened. Hypotheses H-3 and H-5, though quite different from another, involve wrongdoing by David Darling. Conjectures H-1, H-2, and H-4 do not involve any wrongdoing by David Darling. If you are a trial lawyer, David Darling is your client; and if you are instead a police detective, David Darling is on of your suspects in the possibly-criminal death of Victim. But whether you are a trial lawyer or whether you are a police detective, given the evidence known to you, you believe that the probabilities of conjectures H-1 through H-5 are roughly as follows:

P(H-1) = .1
P(H-2) = .05
P(H-3) = .4
P(H-4) = .2
P(H-5) = .05

Question 1. If you are a rational trial lawyer or police detective, which of your five conjectures should you investigate?

Question 1A. If you are a rational trial lawyer or detective, does it follow that it is irrational for you to investigate hypothesis H-2? On what assumptions?

Question 2. If David Darling was convicted of killing David Darling and police detectives investigated only hypothesis H-3, have Darling's due process rights been violated?

Cf. Arizona v. Youngblood, 488 U.S. 51 (1988).

Note: Larry Youngblood was released in the year 2000 -- after new technology -- a new type of DNA test -- convincingly demonstrated that Youngblood had not in fact committed the child molestation crimes for which he was convicted. See Barbara Whitaker, DNA Frees Inmate Years after Justices Rejected Plea, New York Times, August 11, 2000, Friday, Late Edition - Final, Section A; Page 12; Column 1; National Desk. Larry Youngblood spent roughly 17 years in prison for crimes that he very probably did not commit.