You cannot dissociate probing from a legitimate failed payment attempt. If you could, then you could just prevent it in the first place.
To expand a bit more:
the node for which you don't have the secret key (obviously)?
There is no secret key. There is a payment preimage, the preimage to the hash used in the forwarded HTLC.
Is it possible that some of the local fails are probing payments addressed to the node [...]?
If by "the node" you are referring to your node, no. It would be WIRE_INCORRECT_OR_UNKNOWN_PAYMENT_DETAILS.
If you are referring to the next node, it might. According to the protocol it must send an incorrect_or_unknown_payment_details error. But you wouldn't be able to tell them if they didn't respect the protocol, and instead sent a temporary_channel_failure.
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