Q:

p(A|B) where A is not an event, but a real number in [0,1]

I ran into some notation in an article I'm reading, and I can't figure out what the author is trying to say. 
Specifically, say I'm flipping a coin with unknown probability $\omega_H$ of getting heads.  Say $T$ is the event of me flipping the coin and getting tails.  What on earth does it mean to say $p(\omega_H|T)$?  This is the exact notation used in the article, and in the surrounding text the author is talking about Bayesian updating. 
As far as I know, to use Bayes's Theorem with expressions like $p(A|B)$, $A$ and $B$ have to be events that either happen or don't happen, not arbitrary values. 
Does anyone know what this author is trying to say? 

A:

(The article at your link doesn't display properly in my browser.  Here is a more-readable version.)  
The main source of confusion seems to be your thinking that $p(\omega_H\mid T)$ denotes a probability, whereas it is, rather, a (posterior) probability density function of a continuous random variable $\widetilde{\omega}_H$. Another source of confusion may be that the author uses the same symbol for a random variable as for its values.  To distinguish them, here I'll put a tilde on the random variable (i.e., $\widetilde{\omega}_H$) and use ${\omega}_H$ (without the tilde) to denote a value of the random variable. 
Here's the relevant part of the article:

For a binary question, one may interpret
  the model as follows.  Each respondent
  privately and independently conducts one
  toss of a biased coin, with unknown probability
  $\omega_H$ of heads.  The result of the toss
  represents his opinion.  Using this datum, he
  forms a posterior distribution, $p(\omega_H\mid t^r)$, whose
  expectation is the predicted frequency of
  heads.  For example, if the prior is uniform,
  then the posterior distribution following the
  toss will be triangular on $[0,1]$, skewed
  toward heads or tails depending on the result
  of the toss, with an expected value of onethird
  or two-thirds.  

The author uses $t^r$ to denote the $r$th respondent's truthful answer to a single $m$-choice question, represented by a vector whose components are all $0$ except for a $1$ in the position of the choice.  So, for a binary question, $t^r$ is either $(0,1)$ or $(1,0)$ (corresponding to, say, Tail or Head, respectively).  
Thus, the unknown parameter $\widetilde\omega_H$ has an assumed prior distribution described by a probability density function $p(\omega_H)$, and the additional information provided by the value of $t^r$ will "update" this to a posterior density function $p(\omega_H\mid t^r)$ in the usual Bayesian manner. 