probability of an event with independent estimates

[jones34]

I'm looking for either help or pointers to relevant information
regarding what i suspect is a simple question for people who
understand probability.

I want to estimate the probability of an outcome in a sample space of
two events: A and Not A.

I have 2 or more independently derived estimates. for example:

Method 1 says A is likely with 99% probability.
Method 2 says A is likely with 95% probability.
Method 3 says A is likely with 88% probability.

If 1, 2 and 3 are truly independent methods of estimating P(A), I
would expect that they might be combined to produce an estimate of A
with greater than 99% probability. Is that possible, and if so, can
someone point me to a reference for how to calculate the P(A) given
the combination of the three estimates?

Thanks much for your help.

Larry