Efficient routing and wavelength assignment (RWA) in wavelength-routed all-optical networks is critical for achieving high efficiency over the backbone links. Extensive research has been conducted to find strategies to solve the RWA problem with exact network state available at the time of path selection. We consider the problem of minimizing the blocking probability in an all-optical network with partial wavelength conversion and with imprecise network state information. We model imprecision in link-state information (wavelength availability) probabilistically and use Markovian analysis to predict the availability of each link based on its previous advertisement and the estimated average traffic over the link. The estimated probabilities are then used to find the most probable path between a source destination pair. We also consider the problem of lightpath establishment with 1+1 protection. We use the same Markovian model to predict the link availability and then use the probabilistic estimate and a modified version of flow algorithm to find two link-disjoint paths between the source and destination. Simulations are conducted to compare the performance of random-fit and the proposed wavelength assignment schemes. We have also performed extensive simulations to study the performance of the proposed flow algorithm. It is observed that the proposed wavelength assignment scheme performs significantly better in terms of blocking probability than conventional wavelength assignment schemes.