How to detect the match precision of OneVsRestClassifier
Yes, of course. 

Assuming that you have used sklearn's OneVsRestClassifier and so you have a decision function for example a Support Vector Classifier with say linear kernel. Use set_params to change probability key to True, default is False. Use this in the OneVsRestClassifier classifier and then go with the inbuilt function predict_proba like

from sklearn.multiclass import OneVsRestClassifier
from sklearn.svm import SVC
mod = OneVsRestClassifier(SVC(kernel='linear').set_params(probability=True)).fit(samples,classes)
print mod.predict_proba(np.array([your_sample_vector]).reshape(1,-1))


Edit:

You can use your old LinearSVC with decision_function to find the distance from the hyperplane and convert them to probabilities like

mod = OneVsRestClassifier(LinearSVC()).fit(sample,clas)
proba = (1./(1.+np.exp(-mod.decision_function(np.array(your_test_array).reshape(1,-1)))))
proba /= proba.sum(axis=1).reshape((proba.shape[0], -1))\
print proba


Now you don't need tuning the parameters, I guess. :)