What hole size for test probe to get a snug fit?
Normally the hole size you specify in your EDA program will be the finished hole size within some tolerance. 

However, there are a (very) few manufacturers who interpret this as the tool size, so the hole may be somewhat different in size (-0.1mm in the case of one supplier) so it's best to check with your manufacturer. 

For round holes you definitely don't want the minimum hole size to intersect with the maximum pin diameter.