The RaM"a (Y"D 87:6) cites an opinion that one may shouldn't stoke a flame beneath a non-Jew's pot, for fear that there's some milk and meat residue in it, and you might come to cook said milk and meat residue.
R' Akiva Eiger there asks why this should be forbidden considering that there's really a doubt if there is any residue and you don't intend to cook it if it's there. He answers that it's a Pesik Resheih (inevitable consequence), and the doubt relates to the past (whether the pot has milk and meat residue from previous cooking), not purely to the present/future (whether your action will cook meat and milk together), and in that case a simple Safek (doubt) isn't enough to overcome the defining characteristic of a Pesik Resheih, which is its inevitability.
(Pesik Resheih is confusing enough without adding DeLa'Avar to it, so I hope the above was clear.)
If this is so, are there other cases like this in which a Safek DeLa'Avar is deemed inconsequential, and a Pesik Resheih is declared and said action is forbidden? Are there any cases that contradict this (either within R' 'Akiva Eiger's own writings or just in rulings by others who don't hold this opinion)?