A small but fascinating point of general interest arises in The Queen v Khazaal  HCA 26 (10 August 2012). If a defendant has the evidential burden of showing an innocent purpose, can evidence of general good character be sufficient to meet that burden?
The defendant in Khazaal compiled articles from other authors, edited them with his own introduction and published them under a pseudonym as an electronic book. The book contained advocacy of violence, but Mr Khazaal had a statutory defence if his publication was not intended to facilitate assistance in a terrorist act (see  and  of the joint judgment). The evidential burden here means the burden of adducing or pointing to evidence that suggests a reasonable possibility that his purpose was innocent.
Mr Khazaal suggested that his purpose was scholarly and peaceful, and he relied partly on the book itself to meet his evidential burden. The High Court unanimously held that the evidence relied on was not inconsistent with the alleged purpose of facilitating violence (French CJ at , Gummow, Crennan and Bell JJ at , Heydon J at ). Mr Khazaal also relied on his past pursuit of lawful activities as a journalist and argued that the book was written in that vein, however there was insufficient evidence to support that connection .
So, more generally, when does evidence of good character tend to prove a matter in issue? The New Zealand Supreme Court looked at this in Wi v R  NZSC 121, holding that absence of previous convictions has sufficient probative force to meet the requirement of relevance (s 7 of the Evidence Act 2006) but in a particular case it may have only a slight tendency to prove a matter of consequence . I mentioned Wi in the update to my note on Maye v R (Jamaica)  UKPC 35.
Just a little bit of probative value is sufficient to meet the relevance requirement. This does not mean that almost anything goes, because the court can exclude evidence under s 8 if its prejudicial effect outweighs its probative value. Would that little bit of probative value be sufficient to meet the evidential burden of raising a defence? How much "tendency to prove" does the evidential burden require. Probably this is best expressed as a tendency sufficient to raise a reasonable possibility that the issue favours the defendant.
Here we drift further from the facts of Khazaal, like French CJ's ships passing in the night . Imagine that 10% of scholars support violence, and 90% do not. Does evidence that D is a scholar mean that we can be 90% sure he does not support violence? Of course not. Relevance must not be confused with probative value. Yes, evidence that D is a scholar is relevant in the sense that D is using it to support the proposition that it tends to suggest he is not advocating violence. But the probative value (ignoring the separate question of rebuttal by evidence that D's actual writing did in fact advocate violence) of being a scholar requires consideration of different things.
First, one looks at the population of people who advocate violence, and asks what proportion of them are scholars. Then one looks at the population of people who do not advocate violence, and asks what proportion of them are scholars. This allows one to compare the proportion of scholars among the advocates of violence with the proportion of scholars among peaceful people. That tells one whether being a scholar is more consistent with advocating violence than it is with being peaceful. The probative value of the fact of D being a scholar is this comparison of proportions.
This is not how judges reason, but the result is the same in Khazaal. French CJ pointed out that mere consistency with innocent purpose is insufficient to tend to prove innocent purpose -. That is, scholars exist in both the population of advocates of violence and peaceful people, and their existence among peaceful people does not of itself have probative value for the proposition that D was peaceful. I suspect that he was wrong to adopt McClennan CJ at CL's phrase "the evidence ... was entirely neutral", because really the evidence was incomplete: it needed a context. The Court wanted more information about D's scholarly writing and about whether that was consistent with the writing which was the subject of the allegations.
It is appropriate to reject general probabilistic reasoning when specific evidence relevant to a particular case can be obtained. This is the Schrödinger's cat metaphor: once the box is opened and we look inside, the cat's being dead or alive is no longer a question of probabilities. If D kept the box closed, he needed to assist the court more with probabilities, and if he opened the box, he needed to demonstrate that this writing was in line with his other work.