Autodesk Kaydara 3D format (*.fbx files) is supported mainly in various Autodesk software so if you are looking for a way to convert FBX to ASE your best bet would be 3D Studio Max. May require a plugin of sorts, to add support for Kaydara.
Convert Autodesk Kaydara 3D data exchange format to 3D Studio Max ASCII scene export data.
We found one software available in the database for this conversion.
Microsoft Windows software - convert fbx to ase on Windows
A widely-used 3D animation application from Autodesk
Convert from fbx file format
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.